  Previously, the authors reported direct evidence of channel saturation and
conductance quantization in atomic-sized gold constrictions through mechanical
perturbation studies, and also showed that peaks in conductance histograms are
insufficient in evaluating their mechanical stability [Armstrong et al., Phys.
Rev. B 82, 195416 (2010)]. In the present study, gold constrictions spanning
the range from quantum to the semi-classical (Sharvin) conductance regimes are
mechanically probed with pico-level resolution in applied force and
deformation, along with simultaneous measurements of conductance. While
reconfiguration from one constriction size to another is known to occur by
apparently random discrete atomic displacements, results reveal a remarkable
simplicity - the magnitude of discrete atomic displacements is limited to a
small set of values that correspond to elementary slip distances in gold rather
than Au-Au inter-atomic distance. Combined with measurements of spring constant
of constrictions, results reveal two fundamental crossovers in deformation
modes with increasing contact diameter - first, from homogeneous shear to
defect mediated deformation at a diameter that is in close agreement with
previous predictions (Sorensen et al., Phys. Rev. B 57, 3283 (1998)]; second,
the discovery of another crossover marking surface to volume dominated
deformation. A remarkable modulus enhancement is observed when the size of the
constrictions approaches the Fermi wavelength of the electrons, and in the
limit of a single-atom constriction it is at least 2 times that for bulk gold.
Results provide atomistic insight into the stability of these constrictions and
an evolutionary trace of deformation modes, beginning with a single-atom
contact.
