Stability and Rupture of an Ultrathin Ionic Wire

Using a combination of in situ high-resolution transmission electron microscopy and density functional theory, we report the formation and rupture of ${\mathrm{ZrO}}_2$ atomic ionic wires. Near rupture, under tensile stress, the system favors the spontaneous formation of oxygen vacancies, a critical step in the formation of the monatomic bridge. In this length scale, vacancies provide ductilelike behavior, an unexpected mechanical behavior for ionic systems. Our results add an ionic compound to the very selective list of materials that can form monatomic wires and they contribute to the fundamental understanding of the mechanical properties of ceramic materials at the nanoscale.

Figure 1

HRTEM images of the ${\mathrm{ZrO}}_2$ wire near rupture and Zr-Zr distance of $m\text{−}{\mathrm{ZrO}}_2$ bipyramidal cluster calculated from AIMD simulations. Notice that only Zr atoms can be easily distinguished as dark spots in HRTEM images (oxygen atoms are invisible) [20]. (a) An atomic wire is seen with a $\mathrm{Zr}\text{−}{\mathrm{O}}_2$-Zr distance of 3.8 Å. (b) Complex atomic rearrangements take place, as suggested by the yellow triangle displacement indicated in the figure, leading to the formation of an oxygen vacancy at the atomic wire with an increased Zr-O-Zr distance of 4.2 Å, which evolves to 4.3 Å in (c), before rupture and (d) surface reconstruction. (e) Zr-Zr distance at the atomic wire calculated from AIMD simulations at room temperature vs simulation time. The insets show the structure of the $m\text{−}{\mathrm{ZrO}}_2$ cluster at the indicated time frame. Inset (i) shows the initial setup after thermal equilibration at 300 K. As pulling simulation evolves, the Zr-Zr distance at the nanobridge remains roughly constant until (ii), when the atomic rearrangements leading to oxygen vacancy formation start to take place. At (iii), the oxygen-deficient atomic wire is formed, evolving with increasing tensile strain until Zr-O-Zr distances of approximately 4.56 Å, at (v), when rupture occurs.

Figure 2

(a) DFT calculations showing the ${\mathrm{ZrO}}_2$ wire energy ($\mathrm{\Delta }E$) vs unit cell length (with respect to equilibrium unit cell of the perfect wire) for the wire with (orange and green curves) and without (blue curves) an oxygen vacancy until complete rupture. The oxygen chemical potential is added to the total energy of the defective system in two extreme limits: O-rich (orange) and O-poor (green) conditions. The curves are parabolic fits to the last three DFT data points to improve the description of the rupture. The constant-length thermodynamic constraint is represented by the red circle and triangle for each chemical potential limit. The constant-force thermodynamic constraint is represented by the dashed lines in each chemical potential limit. (b) DFT calculations showing the ${\mathrm{ZrO}}_2$ wire deformation curve for the stoichiometric and nonstoichiometric model until complete rupture. At each step, the shaded atoms (as shown in the insets) are fixed and the remaining atoms are allowed to relax. The force is taken on the fixed atoms at each ground-state geometry. The insets show the maximum Zr-Zr distance reached before the atomic-wire rupture. Rupture occurs after the last relaxation step (last point drawn). Comparing the two curves, we notice that the presence of an oxygen vacancy significantly decreases the force required to break the atomic wire and also allows for much longer wire extensions before rupture.