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Intensive or size-invariant physical properties are well known to becomesize-dependent when the bulk material is reduced to the nanometer scale. Usingsilver, the present study shows a remarkable emergent characteristic ofextensive properties as the size of the system is increased from a single atomto bulk - the property (strength) evolves in a staircase manner, as opposed tothe intuitively assumed continuous approach to a saturating bulk value. Inother words, the observed variation with size retains the inherent trait ofintensive properties in the form of size-independent staircase plateaus. Thesteps can be explained by simple and necessary geometric configurations thatatoms must assume in their initial approach to bulk. Were it not for theseobservations, it would have been remarkable to have reported that the observedstrength in the limit of a single-atom Ag bridge approaches the theoreticallimit, being 3-4 orders of magnitude higher than in bulk single crystals. Theappearance of steps is acutely sensitive to minute perturbations, and theirobservation is enabled by pico-level resolution in measured forces anddisplacements in highly stable atomic sized bridges. However, suitablyharnessed, results open the possibility to impart vastly different strengths tothe same material based only on its size. This combined with possibility tochange the position and height of the steps by mixing elements of differentdiameters and surface energy, opens a realistic approach to 'materials bydesign'. Results also provide an example of the evolutionary trace of anemergent physical property in materials.

Stepwise emergence of an intensive physical property from a single-atom to bulk