Nanodisturbances and nanoscale deformation twins in fcc nanowires

The nanodisturbance deformation mode is theoretically described as a specific physical mechanism of plastic flow in nanowires with a fcc crystal structure. The mode represents formation and evolution of nanodisturbances—nanoscopic areas of ideal plastic shear with tiny shear vectors—in mechanically loaded nanowires. We calculated the energy and stress characteristics for the formation of both isolated nanodisturbances and their groups (whose evolution results in nucleation of deformation twins) in Au and Cu nanowires having square cross sections. It is shown that the nanodisturbance deformation mode tends to dominate over conventional dislocation generation and glide in Au and Cu nanowires (with flat free surfaces) at high stresses and zero temperature. In these nanowires, the critical stress for the formation of isolated nanodisturbances and that for nucleation of deformation twins is sensitive to the nanowire width. The sensitivity corresponds to the “smaller is stronger” tendency.

Figure 1

Plastic deformation modes in nanowires. (a)–(e) Conventional partial dislocation slip. (a) Initial state. (b)–(e) Conventional partial dislocation with Burgers vector b is generated at the nanowire free surfaces (where steps of width $b$ are formed) and slips towards opposite free surfaces. A stable stacking fault (SF) joins the dislocation and the free surfaces at which the dislocation was generated. (f)–(j) Nanodisturbance deformation mode (three-dimensional view). (f) Initial state. (g) and (h) Immobile noncrystallographic dislocation is generated. Its Burgers vector magnitude $s$ gradually increases, and a generalized stacking fault (gray region) is formed (and evolves in parallel with the growth of $s$) between the dislocation and free-surface steps. (i) The partial dislocation transforms into a conventional partial dislocation (when $s$ reaches the magnitude $b$ of the Burgers vector of a conventional partial dislocation) and then moves toward the opposite free surfaces. (j) The final structure with surface steps of width $b$ is formed. (k)–(o) Two-dimensional view of the nanodisturbance deformation mode in a crystallographic plane (containing slip line $\mathit{AD}$) of a nanowire with a cubic elementary cell containing atoms of two sorts (full and open circles).

Figure 2

Nanodisturbance deformation mode in the limiting situation where a nanodisturbance occupies a whole area of a nanowire section. In this situation, the nanodisturbance consists of only a generalized stacking fault and produces steps at the nanowire free surface, while noncrystallographic dislocations are absent.

Figure 3

Geometry of edge dislocation in nanowire (shown schematically). (a) The square nanowire section is parallel with the nanowire base and contains the dislocation line $\mathit{BC}$. (b) Slip plane of the dislocation $\mathit{BC}$.

Figure 4

Maps of the energy change $\Delta W_n(x,s)$ in the case of a Au nanowire (with size $d=1\hspace{0.5em}\mathrm{nm}$) under the external shear stress (a) $\tau =3\hspace{0.5em}\mathrm{GPa}$, (b) $\tau =4\hspace{0.5em}\mathrm{GPa}$, and (c) $\tau =4.8\hspace{0.5em}\mathrm{GPa}$. The values of $\Delta W_n$ are given in units of ${\mathrm{Db}}^3$.

Figure 5

Maps of the energy change $\Delta W_n(x,s)$ in the case of a Au nanowire (with size $d=10$ nm) under the external shear stress (a) $\tau =1\hspace{0.5em}\mathrm{GPa}$, (b) $\tau =2.2\hspace{0.5em}\mathrm{GPa}$, and (c) $\tau =2.9\hspace{0.5em}\mathrm{GPa}$. The values of $\Delta W_n$ are given in units of ${10}^2\hspace{0.5em}{\mathrm{Db}}^3$.

Figure 6

Generation of a crystallographic partial dislocation and a noncrystallographic dislocation (through the nanodisturbance mechanism) in a nanowire with preexisting steps on the free surface. (a) Initial configuration with steps $P$ and $Q$. (b) Crystallographic partial dislocation is generated at step $P$, and nanodisturbance is generated at step $Q$. As a result, step $P$ disappears (with the assumption that its initial width is equal to the dislocation Burgers vector magnitude), and the step $Q$ width is decreased by the shear magnitude $s$ characterizing the nanodisturbance.

Figure 7

Map of the energy change $\Delta W_n^{*}(x,s)$ in the case of a Au nanowire with size $d=10\hspace{0.5em}\mathrm{nm}$ under the external shear stress $\tau =1.2\hspace{0.5em}\mathrm{GPa}$. The values of $\Delta W_n^{*}$ are given in units of ${10}^2\hspace{0.5em}{\mathrm{Db}}^3$.

Figure 8

Generation of twin nucleus by the nanodisturbance mode in a nanowire: Two-dimensional view in a crystallographic plane of a nanowire with a cubic elementary cell containing atoms of two types (full and open circles). (a) The nanowire is in its initial state with stable stacking fault $\mathit{AB}$ (which may result from the evolution of a previously generated nanodisturbance). (b) and (c) A nanodisturbance $A^{\prime }{B}^{\prime }$ is generated and evolves in a crystallographic plane neighboring the preexisting stacking fault. (d) The nanodisturbance transforms into a stable stacking fault (neighboring the preeexisting stacking fault). As a result, a nanoscale twin nucleus is generated that consists of two stable stacking faults $\mathit{AB}$ and $A^{\prime }{B}^{\prime }$.

Figure 9

Maps of the energy change $\Delta W_t(x,s)$ in the case of a Au nanowire (with size $d=1$ nm) under the external shear stress (a) $\tau =2.8\hspace{0.5em}\mathrm{GPa}$, (b) $\tau =3.8\hspace{0.5em}\mathrm{GPa}$, and (c) $\tau =4.5\hspace{0.5em}\mathrm{GPa}$. The values of $\Delta W_t$ are given in units of ${\mathrm{Db}}^3$.

Figure 10

Maps of the energy change $\Delta W_t(x,s)$ in the case of a Au nanowire (with size $d=10$ nm) under the external shear stress (a) $\tau =1\hspace{0.5em}\mathrm{GPa}$, (b) $\tau =1.8\hspace{0.5em}\mathrm{GPa}$, and (c) $\tau =2.4\hspace{0.5em}\mathrm{GPa}$. The values of $\Delta W_t$ are given in units of ${10}^2\hspace{0.5em}{\mathrm{Db}}^3$.

Figure 11

Generation of a twin nucleus by the dislocation mechanism in a nanowire: Two-dimensional view in a crystallographic plane of a nanowire with a cubic elementary cell containing atoms of two types (full and open circles). (a) The nanowire is in its initial state with stable stacking fault $\mathit{AB}$. (b) and (c) A partial dislocation glides on a crystallographic plane neighboring the preeexisting stacking fault. (d) The dislocation glide is complete, in which case a nanoscale twin nucleus (consisting of two stable stacking faults $\mathit{AB}$ and $A^{\prime }{B}^{\prime }$) is generated.

Figure 12

Dependences of the critical stress ${\tau }_c$ (the smallest stress at which the nanodisturbance deformation mode occurs in the nonbarrier way) on the nanowire size $d$ in (a) Au and (b) Cu nanowires. Solid curves correspond to the formation of an isolated nanodisturbance. Dashed curves correspond to the formation of a nanoscale twin nucleus.

Figure 13

Crack growth in a composite solid with nanowires (shown schematically). Metallic nanowires are under plastic deformation in the wake of brittle crack tip. They hamper crack growth.