  Intensive or size-invariant physical properties are well known to become
size-dependent when the bulk material is reduced to the nanometer scale. Using
silver, the present study shows a remarkable emergent characteristic of
extensive properties as the size of the system is increased from a single atom
to bulk - the property (strength) evolves in a staircase manner, as opposed to
the intuitively assumed continuous approach to a saturating bulk value. In
other words, the observed variation with size retains the inherent trait of
intensive properties in the form of size-independent staircase plateaus. The
steps can be explained by simple and necessary geometric configurations that
atoms must assume in their initial approach to bulk. Were it not for these
observations, it would have been remarkable to have reported that the observed
strength in the limit of a single-atom Ag bridge approaches the theoretical
limit, being 3-4 orders of magnitude higher than in bulk single crystals. The
appearance of steps is acutely sensitive to minute perturbations, and their
observation is enabled by pico-level resolution in measured forces and
displacements in highly stable atomic sized bridges. However, suitably
harnessed, results open the possibility to impart vastly different strengths to
the same material based only on its size. This combined with possibility to
change the position and height of the steps by mixing elements of different
diameters and surface energy, opens a realistic approach to 'materials by
design'. Results also provide an example of the evolutionary trace of an
emergent physical property in materials.
