Conductance of atom-sized contacts of dilute Al alloys

We have measured the conductance of atom-sized contacts of some dilute Al alloys in ultrahigh vacuum at room temperature. Measurements on Al-1.1at%Si, Al-2.8at%Mg, and Al-1.1at%Mg-0.6at%Si show no significant alloying effects: their conductance histograms are substantially the same as that of pure Al and exhibit a first peak corresponding to the single-atom contact of Al. On the other hand, a multicomponent Al alloy, Al-4.2at%Zn3.6at%Mg-0.7at%Cu-0.01at%Ag (“meso10”), yields a conductance histogram which is totally different from others and shows no single-atom conductance peak of Al. We consider that in this high-strength alloy, the influence of alloying on the conductance would be mechanical rather than electronic. [DOI: 10.1380/ejssnt.2009.741]


I. INTRODUCTION
Atom-sized contacts of metals are prototypical ballistic metal contacts and known to exhibit a variety of unique electronic and mechanical properties that are not observed in macroscopic contacts [1].Particularly noteworthy is the conductance of single-atom contacts (SACs), which is determined by the transmission characteristics of those electronic states ("conductance channels") of SAC that contribute to the electron transport.For pure metals, it is theoretically predicted [2] and experimentally demonstrated [3,4] that the SAC conductance of each metal primarily depends on the valence states of that metal.Monovalent metals, such as Au, Ag, and Cu, for example, have a single conductance channel of s-like characteristics in their SAC state.This channel achieves a high electron transmission and, following the Landauer formula, yields the SAC conductance in good agreement with G 0 = 2e 2 /h, the quantum unit of conductance.On the other hand, the SAC of trivalent Al has three conductance channels.One channel of sp z characteristics is highly transparent while other two channels of p x − p y characteristics are nearly closed [2,5].In experiment, the SAC conductance of Al is (0.8 − 0.9)G 0 [6][7][8][9].
Atom-sized contacts are usually fabricated by the socalled break junction method where a pair of macroscopic electrodes are first brought into contact to form a junction and then separated apart to break it.During the junction break, the contact point of the junction makes a necking deformation and shrinks to the size of atoms.Occasionally, an SAC forms just before the junction failure.Because we have no precise control over the necking deformation of nano-sized junctions, each breakage yields a variety of SAC geometries and conductance values.Statistical treatment of the conductance is thus necessary and usually carried out by repeating junction breakage a large number of times and summing up the conductance data into a conductance histogram.In most cases, the conductance histogram shows a couple of peaks, and the first peak (the lowest conductance peak) is usually attributed to SAC.From the position of this SAC peak, we can determine the SAC conductance.The conductance histogram of noble metals, for example, exhibits a sharp SAC peak at 1G 0 , while the Al SAC peak appears at (0.8 − 0.9)G 0 [6][7][8][9], reflecting the partial transmission of the conductance channels.
In the case of alloys, solute atoms affect the conductance histogram of pure metals in two ways, electronic and mechanical.Electronic effects are electron scattering by solute atoms and modification of the electronic structure of a host metal by alloying.These electronic effects are considered to produce a shift and/or broadening of the SAC peak in the histogram.For noble metals, however, no such electronic effects are found in the past experiments.Hansen et al. [10] showed that the conductance histogram of Au-5at%Co is essentially the same as that of pure Au.Subsequent measurements covering a full range of solute concentration on AuPd and AuAg [11] and on CuNi alloys [12] indicate that the conductance histogram of pure Au gradually changes with alloying but well preserves its peak features up to ∼50at%.Particularly, no appreciable shift of the SAC peak is observed.These observations clearly suggest that the SAC conductance of noble metals is insensitive to dilute alloying and affected only when the SAC site is occupied by a solute atom (the locality of the SAC conductance is also demonstrated by Heemskerk et al. [13] on Au-50at%Pt).This apparent immunity of the SAC conductance against alloying is attributed to the s-like valence electron of noble metals, which enables electrons to detour blocking solute atoms locating nearby the contact site.
The other alloying effect is a mechanical effect.Alloying generally strengthens a host metal, and this influences the formation of SAC in a break junction.Because SACs are formed by necking deformation, hard metals are naturally supposed to produce SACs less frequently than soft metals.This hardening effect has been observed for some refractory metals [14,15] but not yet been fully explored for alloys.Fujii et al. [16] report that the SAC peak of a hard Au-20at%Pt vanishes at lower bias compared to that of soft Au-17at%Ag and Au-26at%Cu alloys.Below 0.3 V, however, these alloys yield almost the same conductance histograms, and the mechanical effect on the conductance histogram of Au alloys is yet unclear.
In this work, we studied alloying effects on the conductance histogram of Al atom-sized contact.We took up Al alloys because the SAC conductance of Al is ex- pected to be more susceptible to electronic and mechanical alloying effects than that of noble metals.First, the Al SAC conductance sensitively depends on the atomic arrangement and decreases with slight contact distortions [5,17].High-transmission pathways detouring solute atoms, available for electrons in noble-metal SACs, do not exist in Al SACs.Second, Al alloys undergo substantial hardening by adding a small amount of solutes.However, no experiments on Al alloys have been performed before, perhaps because of the difficulty in preparing Al alloy specimens covering a wide range of solute concentration.Most metals have very low solubility to Al, and only dilute Al alloys are practically available.Despite this limitation on the solute level, it appears still worth to study whether solute atoms make appreciable influence on the SAC conductance of Al.In this work, we made an experiment on four dilute Al alloys: Al-1.1at%Si,Al-2.8at%Mg,Al-1.1at%Mg-0.6at%Si,and Al-4.2at%Zn-3.6at%Mg-0.7at%Cu-0.01at%Ag.The last one is a hightensile-strength alloy known as "meso10".We fabricated atom-sized contacts of these alloys, measured their conductance, and compared the results with that of pure Al.

II. EXPERIMENT
For Al-Si, Al-Mg, and Al-Si-Mg samples, we used commercial alloy wires of 0.25-0.3mm in diameter.No heat treatment was applied, so that these wires had probably been long-aged at room temperature.For meso10, we prepared a 0.25-mm-wire by die-drawing a 1-mm-diameter meso10 wire.After forming the wire into U-and J-shaped electrodes, they were annealed at 760 K for 3.6 ks in argon atmosphere and quenched into an iced water.This annealing condition is a standard recipe for the solutiontreatment of meso10, and there should be no residual effects of die-drawing in our meso10 samples.
We employed the same experimental setup described in our previous measurements of the Al SAC conductance [8].Fabrication of atom-sized contacts was made by breaking a macroscopic junction.Instead of the wiredisk junction used in Ref. 8, a wire-wire junction is employed in this experiment.One electrode of the junction is a U-shaped sample wire, two open ends of which are inserted into two holes on a metal base plate and fixed there by a silver paste.A counter electrode is a piece of the same wire which is bent into J-shape.The longer end of this wire is attached to a tubular-PZT/inchworm positioning unit and arranged so that the U-and J-shaped electrodes make a contact at their bent side.This U-J wire-wire junction is repeatedly made open and closed at a rate of 1.74 Hz by moving back and forth the J-shaped electrode with the tubular-PZT.Temporal change in the junction conductance is monitored by measuring a voltage drop V m across a R = 1 kΩ current-sensing resistor connected in series with the junction.An external bias V a is applied to (junction)+R, and the junction conductance is obtained from Note that the true bias V b across the junction is lower than V a and given as V b = V a − V m .This difference between V a and V b varies with the junction conductance and becomes 7% when G = 1G 0 .
Our method of making junction is the so-called "hard indentation type", where the electrodes are brought into a hard crash contact to ensure low initial resistance.Because of this, no in situ sample cleaning was performed other than brushing off oxides and cleaning the sample wires in ethanol before loading them into a vacuum chamber.All measurements were carried out at room temperature in ultrahigh vacuum better than 5 × 10 −8 Pa.To achieve this ultrahigh vacuum condition, the chamber is baked overnight at 393 K.This baking resulted in unintentional sample annealing, the effect of which will be discussed in Sec.IV.

III. RESULTS
Examples of the conductance trace are shown in Figs.1(a) and (b) for the Al-Mg and meso10 alloys, respectively.As is usually observed in breaking contacts of other metals, the conductance decreases discontinuously and exhibits a couple of plateaus/steps, indicating a discrete nature of the contact deformation in its final stage.These conductance plateaus correspond to certain stable contact geometries.In Fig. 1(a), the last conductance plateau appears at ∼ 0.7G 0 in near agreement with the SAC conductance of Al.This plateau, therefore, probably corresponds to an Al SAC.In Fig. 1(b), on the other hand, the conductance of a meso10 junction jumps to zero from a plateau locating around 2G 0 .Though some conductance traces show plateaus around 1G 0 or less, majority of the observed traces of meso10 behave like the one shown in Fig. 1(b) and are disrupted around (2 − 3)G 0 .This result suggests that most of meso10 junctions deform to an atom-sized contact of (2 − 3)G 0 in conductance, but cannot shrink further to form an SAC.
We show in Fig. 2 conductance histograms of three alloys, Al-Si, Al-Mg, and Al-Si-Mg alloys obtained at different bias voltages.Note that the bias voltage indicated in each panel is the applied bias V a which is slightly higher than true bias voltage V b as mentioned in the previous section.Histograms obtained on pure Al are also included in the figure for comparison.Measurements were repeated a couple of times, and the total number of conductance trace observed to construct each histogram is 4,000 for pure Al and Al-Si, and 6,000 for Al-Mg, and Al-Si-Mg, respectively.Because the conductance G is calculated from V m as mentioned in the previous section, and the relationship between G and V m is nonlinear, we first made the histogram of V m and then converted its horizontal scale from http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology Volume 7 (2009) V m to G.This equalizes the statistical weight of each column in the histogram but renders the conductance scale slightly nonlinear.The bin width is set to twice as large as the digitizing resolution of V m and (0.26 − 1.02) mV depending on V a .
We first note in Fig. 2 that the conductance histogram of pure Al is in good agreement with that of our previous experiment [8].The SAC peak appears at slightly lower conductance, and this will be discussed later.At 0.1 V, the SAC peak is a bit broadened due to lower S/N ratio at low biases but becomes more prominent at 0.2 and 0.3 V and tends to be suppressed at 0.4 V.The second and third peaks also decrease with increasing the bias and almost disappear at 0.4 V.All these features are the same as observed in our previous experiment.Among three alloys studied in this work, Al-Mg shows the histogram that is almost identical with that of pure Al and exhibits the same bias dependence.No alloying effects are thus observed on the Al-Mg alloy.On the other hand, peak features are more broadened in the histogram of Al-Si and Al-Mg-Si alloys, particularly at 0.1 V. Nevertheless, the SAC peak can be well identified and appears at the same conductance as that of the SAC peak of pure Al and Al-Mg.We can therefore conclude that in these Al alloys, there are no strong alloying effects on the SAC conductance of Al.This result is understandable because our Al-Si, Al-Mg, and Al-Mg-Si samples contain less than 3 at% of solutes.Presumably at this low concentration, solute atoms would be too dilute to affect the SAC conductance of Al, even if the Al SAC conductance is more sensitive to alloying than that of Au and Cu.
A couple of comments should be made on the SAC peak of pure Al and three alloys shown in Fig. 2. First, a shoul-der can be observed at the lower conductance side of the SAC peak of Al-Si and Al-Mg-Si.This feature might be an SAC subpeak downward-shifted by solute scattering.However, the SAC peak of pure Al often shows a similar shoulder or a subpeak [7], and we cannot know whether the shoulder is a genuine feature of Al or an alloyinginduced subpeak.Second, the SAC peak in histograms in Fig. 2 appears at ∼ 0.7G 0 , which is slightly lower than the SAC conductance of pure Al [6][7][8][9].This is certainly not an alloying effect because the SAC peak of pure Al also appears at ∼ 0.7G 0 in Fig. 2. Such a systematic peak shift to the lower conductance side is often observed in other metals and usually referred to an apparent "residual resistance" (or "lead resistance") of a contact.If the observed peak shift is entirely due to the residual resistance, its magnitude would be ∼ 1 kΩ.Although a residual resistance of the order of 500 Ω is often observed in previous experiments [10], the estimated residual resistance in this experiment is even higher and may contain some additional contributions.Because the only difference between this experiment and Ref. 8 lies in the junction geometry, i.e. the U-J wire-wire junction in this experiment instead of the wire-disk junction in ref. 8, the additional resistance is likely to come from the use of wire-wire junction in this experiment.It, however, remains unclear why the wire-wire junction tends to yield higher residual resistance than the wire-disk junction.
In the case of meso10 alloy, our measurements yielded totally different results.Figure 3 shows conductance histograms of meso10 alloy obtained at V a = (0.1 − 0.4) V. Histograms are constructed in the same manner as we used for histograms in Fig. 2. We made measurements on two samples and obtained 10,000 conductance traces in total to produce each histogram.Clearly, the histogram of meso10 shows peak features that are quite dissimilar to in those of pure Al and three dilute alloys shown in Fig. 2. At all biases, the SAC peak of pure Al is missing and replaced by a broad maximum centered around 2.5G 0 .
A shoulder-like feature can be observed around 1.2G 0 at 0.1 V, but it submerges into background at higher biases.The position of the new broad peak roughly corresponds to the last conductance plateau shown in Fig. 1(b), and similar plateaus appearing at slightly different positions are likely to produce this broad peak.With increasing the bias, the broad peak decreases in height, becomes more flattened, but still remains visible at 0.4 V, contrary to the second and third peaks in histograms in Fig. 2 which disappear at 0.4 V. Since the peak occupies a large portion of each histogram, relatively stable contacts should be responsible for this peak.However, there is at present no information on these stable contacts, and their structural details are totally unknown.We note that the nominal solute concentration in meso10 is 8.5 at% in total, which is about three times higher than that of the Al alloys which revealed substantial alloying effects in Fig. 2. It is thus natural to consider that the higher solute level in meso10 should modify the conductance histogram and eliminate the Al SAC peak.We, however, found that the results obtained on meso10 cannot be simply interpreted as we will discuss in the next section.

IV. DISCUSSION
Because most metals have low solubility to Al, solute precipitation and accompanying solute depletion in the matrix are more or less inevitable in many Al alloys.We, therefore, have to first consider the influence of precipitation on the solute concentration of our samples.Except for the meso10 samples, other samples are commercial alloy wires which must be aged at room temperature for long time.Also, the overnight baking of the vacuum chamber at 393 K should yield additional aging as noted in Sec.II.Our Al-Si, Al-Mg, and Al-Si-Mg samples are thus certain to have some precipitates in their matrix.In the case of Al-Si and Al-Mg-Si, Si is insoluble to Al at room temperature so that Si precipitates (probably small Si clusters [18]) are formed in our samples.However, atom-probe analyses of room-temperature-aged Al-Mg-Si alloys [19] indicate that the matrix composition is not much depleted from the nominal value.On the other hand, the solubility of Mg to Al at room temperature is 2 at% [20].Thus, our Al-2.8at%Mgalloy should maintain the Mg concentration of ∼ 2 at% in the matrix.These considerations suggest that the solute precipitation indeed occurs in our Al-Si, Al-Mg and Al-Mg-Si samples but does not yet develop to significantly reduce the solute concentration in the matrix.
Situation is, however, different in our meso10 samples.As we noted in Sec.II, we solution treated the meso10 samples at 760 K to homogenize the solute distribution.Despite this heat treatment, the precipitation is likely to occur, unintentionally, during the baking of the vacuum chamber.Nako et al. [21] aged the solution-treated meso10 specimen at 383 K for 30 hours and found that the matrix composition changes to Al-1.4at%Zn1.1at%Mg0.4at%Cu.Because our baking condition (393 K overnight) is similar to their aging condition, the matrix of our meso10 samples is certainly depleted and should have nearly the same composition as reported by Nako et al.The total solute concentration in the matrix would then become ∼ 2.9 at%, which is comparable to that of Al-Mg.Nevertheless, the conductance histograms of Al-Mg and meso10 are completely dissimilar as shown in Figs. 2 and 3.The new broad feature of the meso10 histogram cannot thus be the result of nominally high solute concentration of meso10, and another explanation must be sought for it.
In Sec.I, we pointed out that alloying would affect the SAC conductance of host metal through electronic and mechanical influences.The electronic effects are unlikely to account for the meso10 histogram because electronic alloying effects generally decrease with the solute level.We consider that the alloying effects which result in the observed meso10 histogram would be mechanical rather than electronic.Because meso10 is a precipitation-hardened alloy, achieving a high tensile strength (790 MPa) comparable to that of hard Ta, hardening effects would not be neglected.Atom-probe and SAXS (small-angle X-ray scattering) experiments [21,22] revealed that the precipitates in meso10 are densely distributed, with a separation of ∼ 8 nm.In such finely precipitated specimens, the deformation of the atom-sized contacts would not be the same as that of ordinary metals.In the break junction, the contact point is heavily deformed when the junction is closed and should contain high density of dislocations.In the case of ductile metals, this deformation can be relaxed during the subsequent junction stretching through successive slip deformation of the contact.However, in the meso10 samples, high volume fraction of precipitates would leave small ductile regions in the matrix and tend to prohibit extensive slip deformations.This precipitation hardening makes the meso10 contacts more likely to fracture before they shrink to an SAC and hence reduces the chance of forming SACs.The conductance jump from ∼ 2G 0 shown in Fig. 1 would be an example of such a premature contact failure.Precipitation hardening should occur in our Al-Si, Al-Mg, and Al-Si-Mg samples as well.However, in these alloys, precipitates are relatively far apart (∼ 100 nm) so that except around precipitates, there would remain a ductile matrix region of relatively low dislocation density.This region is macroscopically very small but still larger than the size of atomic scale contacts.Thus, upon stretching the contact, the ductile region accommodates normal slip deformation and can lead to the formation of Al SAC.We note that in Fig. 2, the SAC peak of Al-Si and Al-Si-Mg is more broadened than that of Al and Al-Mg.This broadening may also be due to precipitation hardening because Al-Si and Al-Si-Mg are more precipitated (with Si clusters) than Al-Mg which is close to the solubility limit and should have lesser precipitates.
The difference in the precipitation morphology and hardening can thus consistently accounts for similarities and differences among conductance histograms of pure Al and Al alloys shown in Figs. 2 and 3.There is, however, no substantial understanding on how metal hardening actually affects the necking deformation of an atomsized contact and the formation of SAC.Yanson and coworkers [9,23] studied effects of work hardening on the conductance histogram of Au and Al.Their analyses are, however, concerned with textured orientation of grains and little related to the hardening effect on SAC discussed above.Fractography with scanning-electronmicroscopy observations is a standard method for investigating fractured materials but can hardly be applied to the premature failure of meso10 contacts because the contact at fracture would become the size of atoms [24].
High-resolution transmission-electron-microscopy [25,26] would be a promising tool for elucidating the hardening effects on the atom-sized contacts, but no observations have yet been made on Al and Al alloys.Presumably, some clues could be obtained from the atomic-scale simulation of Al contact failure [27].With introducing finely dispersed artificial obstacles, mimicking precipitates in a specimen, such a simulation would reveal what actually happens in the break of precipitation-hardened Al alloy contacts.It would also provide us information on the atomic geometry of the stable meso10 contact which is responsible for the plateau in Fig. 1 and the broad peak around 2.5G 0 in Fig. 3.

V. CONCLUSION
By exploiting the wire-wire break junction, we have measured the conductance of atom-sized contacts of some Al alloys.The observed conductance histograms of Al-1.1at%Si,Al-2.8at%Mg, and Al-1.1at%Mg-0.6at%Sialloys are essentially the same as that of pure Al and exhibit no strong influence of alloying.In particular, the SAC conductance peak of Al is well preserved.Clearly, the solute level in these dilute alloys is too low to affect the SAC conductance of Al.On the other hand, the meso10 alloy yields a conductance histogram which is entirely different from others and reveals no SAC peak, even though the solute concentration in the matrix would become depleted by precipitation to the level comparable to that of Al-Mg.We consider it likely that this apparent strong alloying effect in the meso10 is a mechanical effect, where the precipitation-hardened contact leads to a premature fracture of the breaking junction and suppresses the SAC formation.

FIG. 2 :
FIG. 2: Conductance histograms of Al-Si, Al-Mg, and Al-Si-Mg alloys obtained at different applied voltages.Results on pure Al are also shown for comparison.Upper limit of the vertical scale in each panel is 15,000 points for pure Al and Al-Si and 27,500 points for Al-Mg and Al-Mg-Si, respectively.

FIG. 3 :
FIG.3: Conductance histograms of the meso10 alloy obtained at the same condition as those shown in Fig.2.Upper limit of the vertical scale in each panel is 50,000 points.