physica status solid.. - Mechanical and Aerospace Engineering

Rapid
Research Letter
Phys. Status Solidi RRL 6, No. 3 (2012) 101
Strength framework in Refs. [14, 15] appears well suited to
analyze the size dependence of strength and modulus enhancement.
Finally, the inset in Fig. 2(b) shows a zoom-in view of
the strength of Ag, with data from additional experiments.
Remarkably, the data reveals discrete behavior for 1-atom,
and 2-atom bridges (standard deviation of discrete values
shown in blue). The discreteness is due to orientation dependent
variation of the strength because each time a
bridge is formed, forces are measured along different crystallographic
directions relative to the tip and the substrate.
This is known from our previous measurements of discrete
atomic displacements [7]. This is followed by plateaus. Although
discrete values were also observed for Au, plateaus
were not seen. This is because the surface energy of Ag
varies little with crystallographic orientation (~6%), in
contrast to ~33% variation for Au [16]. This causes steps
in Au to smear out. Although samples are constrained between
tip and substrate, the existence of plateaus is analogous
to the islands of stability in free clusters; see for example
Ref. [17] for the behavior of clusters with 3–13 atoms.
The position of steps can be qualitatively illustrated
by simple geometric configurations of atoms with increasing
diameter. As shown schematically in Fig. 3, the 1-, 2-,
and 3-atom configurations are unique and discrete. Once a
3-atom diameter sample is formed, it gives rise to three
equivalent sites, where atoms 4–6 sit (first plateau from
4 atoms to ~6–7 atoms).
1
1
2
1
3
4 5
6
2
1
3 2
4
4 1 5
7’ 3 2
7 6
6-7
5 6 7
4 1 7
3 2
8
13
13
9
12
13
10
11
14
19
19
15 16
4
19
5 6
Figure 3 (online colour at: www.pss-rapid.com) Schematic
showing the atomic configurations to illustrate the occurrence of
plateaus. Arrows and numbers indicate available sites; different
colors are used as aid to illustrate the successive build-up of contact
diameter.
3
2
7
18
17
Once the 1 st ring is complete, positions ‘8–13’
(marked by arrows) are filled to give the 2 nd plateau from
7–13 atoms. The 3 rd plateau from 13–19 atoms is associated
with the formation of complete rings around each
atom (marked 2–7 in the 1 st outer ring). Addition of atoms
14–19 results in completion of the 2 nd outer ring for a total
of 19 atoms. Formation of the 2 nd ring creates 12 new
equivalent positions around it, and the process continues.
Transitions at diameters with 7 atoms, 19 atoms, and
37 atoms have been seen in our recent study on the magnitude
of discrete atomic displacements in Au [7]. However,
a large variation in surface energy with orientation in Au
smears out the steps. Even in Ag, the plateaus are highly
susceptible to perturbations. However, Ag provides a new
distinguishing ‘marker’, in addition to the one recently discovered
in Ref. [8]. In summary, the results open the possibility
to impart vastly different strengths based on the
size. Position and height of steps can be changed by mixing
elements of different size and surface energy, and offers
a realistic approach to ‘materials by design’. The results
also provide evolutionary trace of an emergent intensive
property (strength) – variation with size retains the
inherent trait of intensive properties in form of sizeindependent
steps.
Acknowledgements This work was supported by the National
Science Foundation, Grant Nos. DMR-0706074 and DMR-
0964830, and this support is gratefully acknowledged.
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