Shell structures in aluminum nanocontacts at elevated temperatures
© Costa-Krämer et al; licensee Springer. 2012
Received: 19 August 2011
Accepted: 10 February 2012
Published: 10 February 2012
Aluminum nanocontact conductance histograms are studied experimentally from room temperature up to near the bulk melting point. The dominant stable configurations for this metal show a very early crossover from shell structures at low wire diameters to ionic subshell structures at larger diameters. At these larger radii, the favorable structures are temperature-independent and consistent with those expected for ionic subshell (faceted) formations in face-centered cubic geometries. When approaching the bulk melting temperature, these local stability structures become less pronounced as shown by the vanishing conductance histogram peak structure.
The study of shell structures in metallic nanowires has been a topic of increasing interest during the last few years [1–13]. These shell structures are a close analog to shell structures observed for metal clusters [14, 15]. For alkali metals, it has been observed that the stability of the nanowires formed is influenced by electronic shell filling effects associated with atomic arrangements that produce the closing of electronic shells [1–3]. However, for Na and K at larger diameters, a crossover is found from which shell closings correspond to crystalline facet completion with an additional atomic layer [2, 3]. These shell and subshell effects in nanowires manifest as stability peaks in the conductance histograms as the conductance depends on the wire's minimum cross section. In previous works on alkali metals [1–3], the conductance is measured at about one-third of the metal melting temperature as all the shell effect oscillations were observable at elevated temperatures. However, broad-peak precursors of the electronic shell effect are observed at 4.2 K . In a previous work , clear evidence was presented of an atomic shell structure in gold nanocontacts formed at room temperature (far from the Au bulk melting point 1,340 K). These results confirmed conductance histograms as a powerful tool to study stable configurations of nanostructures.
In this work, conductance histograms for aluminum nanowires are presented at different temperatures, from room temperature [RT] up to near the melting point of the bulk. This explores the influence of temperature on the stable configurations seen by the different shell and subshell structures in these metal nanocontacts. This extends a previous study performed by a different technique at RT .
Results and discussion
The results for the high-conductance region must be interpreted in terms of ionic subshells as for the larger structures, the dominance of crystal fields with respect to electronic effects must occur in all metals. The value of 0.20 ± 0.02 is well explained by optimal sections of a face-centered cubic [fcc] crystal, as previously has been proposed for the gold case at 300 K . In fact, if the lattice structure of the wire is that of the bulk metal (fcc for Au and Al), at a large wire radius, a stable configuration is obtained each time a single facet of the wire cross section is completely covered with atoms, as suggested by Yanson et al. [2, 3]. Two geometries for fcc wires produce similar results . The first one has a hexagonal cross section with an axis oriented in the  direction and six equal area facets, four of which are hexagonally packed. The second energetically favored structure is octagonal, also with the axis along the  direction but with facets of exposed area fractions βijk: β111 = 0.55, β100 = 0.25, and β110 = 0.20 accounting for both surface and edge energies. Using the conductance semiclassical expression, one can compute the conductance, g(n), as a function of the number of complete crystalline layers n. For the hexagonal section, the slope d(g1/2)/dn is 1.427 while 1.844 for the octagonal section. Such slopes are too high to explain the results, but if facets are filled individually, as previously suggested by Yanson et al. [2, 3], the slopes decrease to 0.24 in the first case and to 0.23 in the second case. Both structures approach the measured value. Differences can be explained taking into account that experimentally, nanowires are generated from polycrystalline electrodes, so it is also expected that structures with other atomic arrangements or with an axis along directions different to  can contribute to the experimental value [5–10].
At low conductance values, the slopes seem to change with temperature (see data in the label in Figure 4), although as explained above, these data has to be treated carefully because it depends on the peak indexing procedure. However, it is quite clear that for aluminum, a very early (m ≈ 4) crossover occurs to the ionic shell with fcc geometries for all temperatures; this is different to the gold case at 300 K where the crossover was observed at m ≈ 8 . In alkali metal nanocontacts, the low conductance slopes (between 0.54 for K and 0.62 for Li) have been associated with electronic shells by Yanson et al. [2, 3]. For electronic shells, the results are explained in the semiclassical theory framework which shows that the periodicity is due to closed orbits of the delocalized valence electrons. Accordingly, the slope values are explained as the result of a combination of diametric, triangular, and square orbits (the first three shortest periodic orbits in a circular geometry which make only one revolution around the center). On the other hand, in earlier experiments on Al clusters, Lermé et al.  found a regular shell structure that they attributed to starlike orbits (the ones that make two turns around the center before closing). This orbit leads to a calculated slope of 0.33 to g1/2(m). However, Martin  has also found this regular shell structure in the mass spectrum of cold Al clusters and interpreted it in terms of ionic shells (filling of successive triangular facets of an octahedron). Our results in aluminum nanowires seem to show a slight decrease in the slope with temperature, from about 0.4 to 0.3 at moderate and elevated temperatures, respectively. However, due to the large error in the slope determination, which is partly due to the few points at low conductance, this slope might very well be constant and of about 0.35 for all temperatures. Therefore, our data cannot discern unambiguously the existence of temperature dependence of the g1/2(m) slope at low conductance.
In a previous work , the close correspondence between conductance and the number of atoms in the Al wire cross section was confirmed by comparing Al experimental conductance histograms at RT and the embedded atom in molecular dynamics simulations. Moreover, very recently, we have reported  both experimental results and molecular dynamics simulations of oscillations in Au and Al conductance histograms at RT. The intermediate and even the low-conductance slopes of Al experiments were well explained by the simulations. These results suggested that in Al nanocontacts, electronic shells were not evident at 300 K. Simulations performed by Gülseren et al.  suggest that thin aluminum wires should develop exotic, noncrystalline, stable atomic structures once their radii decrease below a critical size (5.3 Å in this case). Icosahedral packings or helical, spiral-structured wires may dominate these structures. For these wires, the surface energy dominates, resulting in a lower total energy compared to that of crystalline (fcc) wires and have been experimentally observed in gold  and platinum . The experimental evidence presented in this work is not enough to establish if these types of structures are responsible of the behavior at low radii. The behavior is possibly due to a very early crossover between electronic and ionic shell filling effects. More experimental and theoretical studies on Al nanocontacts would be needed to understand the low conductance results.
Evidence of subshell structures in the conductance histograms is presented for Al nanowires in the 300 to 700 K temperature range. The results for this metal imply a very early crossover from shell structures that dominate at a low wire radius to the ionic subshell structure at a larger radius. We have found that the structure at high radii (or conductance) values is independent on the temperature, and the results are consistent with those expected for ionic subshell (faceted) formation in fcc geometries. However, in approaching the bulk melting temperature, these local stability structures become less pronounced as shown by the vanishing conductance histogram peak structure. At low conductance values, a linear relationship between g1/2 versus m is measured, although the data is not good enough to interpret the obtained values in terms of the electronic or ionic shells unambiguously.
This work has been partially supported by a Spanish (CSIC)-Venezuelan (IVIC) researcher exchange program. The authors acknowledge the helpful discussions with Anwar Hasmy, Ernesto Medina, and Pedro A. Serena.
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