Interaction of small mobile stacking fault tetrahedra with free surfaces, dislocations, and interfaces in Cu and Cu-Nb

The presence of stacking fault tetrahedra (SFTs) in face-centered-cubic metals substantially modifies the material response to external loading. These defects are extremely stable with increasing energetic stability as they grow in size. At the sizes visible within a transmission electron microscope, they appear nearly immobile. We have recently shown that these defects might indeed migrate, with defective SFTs exhibiting particularly high mobilities. In this paper, using molecular dynamics, we show how mobile SFTs interact with various types of extended defects, including free surfaces, dislocations, and interfaces in Cu and Cu-Nb systems. We observe a direct relation between the energetics of a single vacancy interacting with each external defect and the propensity for the SFT to be absorbed. Finally, using mesoscale modeling, we show how the fact that SFTs can migrate influences the system evolution and potentially important observables of interest such as the void denuded zones around defect sinks.

Figure 1

12V-SFT interacting with (a) and (b) a $\left\{110\right\}$; (c) and (d) a $\left\{111\right\}$; and (e) and (f) a $\left\{112\right\}$ free surfaces in single-phase Cu. Atoms are colored according to their structure (as determined by a common neighbor analysis): hcp as red, bcc as blue, and unknown structure as white; fcc atoms are not shown for clarity. In panels (a), (c), and (e), the configuration as the SFT first directly interacts with the surface is provided, while the configuration after full absorption of the SFT by each surface is provided in panels (b), (d), and (f). The perspective is from inside the material, viewing the surface from within.

Figure 2

Resulting configuration after the interaction of a $12V$ SFT with (a) an edge dislocation and (b) a screw dislocation in single-phase Cu. Dislocations are split into Shockley partials bounding a stacking fault ribbon. The color coding is the same as in Fig. 1.

Figure 3

(a) and (b) $12V$-SFT and (c) and (d) $18V$-SFT interacting with an asymmetric $\mathrm{\Sigma }11$ tilt grain boundary in Cu. Panels (a) and (c) show the initial interaction of the SFT with the boundary while panels (b) and (d) display the final configuration, after the SFT has been absorbed by the boundary. The color coding is the same as in Fig. 1.

Figure 4

(a) and (b) $12V$-SFT and (c) and (d) $18V$-SFT interacting with a $\mathrm{\Sigma }5$ twist grain boundary in Cu. Panels (a) and (c) show the initial interaction while panels (b) and (d) display the final configuration after absorption. The interface is colored according to ${\sigma }_{xx}$ on each atom calculated with the virial theorem while the SFT is colored according to the atomic structure (hcp and unknown coordination as red and white, respectively).

Figure 5

(a) and (b) $12V$-SFT and (c) and (d) $18V$-SFT interacting with a $4^{\circ } \left\{100\right\}$ twist boundary in Cu. Panels (a) and (c) show the initial interaction of the SFT with the boundary while panels (b) and (d) show the final configuration after absorption. The color coding is the same as in Fig. 1.

Figure 6

Interaction of a $12V$-SFT with a $2^{\circ } \left\{111\right\}$ twist boundary in Cu. (a) Initial interaction; (b) final configuration. The color coding is the same as in Fig. 1.

Figure 7

Final configuration of a $12V$-SFT interacting with a $\mathrm{\Sigma }11$ tilt boundary in Cu. The color coding is the same as in Fig. 4.

Figure 8

$12V$-SFT interacting with a $\mathrm{\Sigma }3$ twin boundary in Cu. The color coding is the same as in Fig. 1.

Figure 9

(a) and (b) Interaction of a 12V-SFT with a KS1 hetero-interface in Cu-Nb. Panel (a) shows the first reaction and panel (b) shows the final interface configuration. (c) and (d) Interaction of a 18V-SFT with a KS1 hetero-interface: Panel (c) shows the first reaction and panel (d) shows the final configuration. The color coding is the same as in Fig. 4. The dark blue regions correspond to the locations of the MDIs within the interface. In this perspective, the view is from inside Cu, looking down on the interfacial plane.

Figure 10

$12V$-SFT interaction with an ARB KS hetero-interface in Cu-Nb. Panel (a) shows the initial interaction and panel (b) illustrates the final interface configuration after the SFT has been absorbed. The color coding is the same as in Fig. 4.

Figure 11

Analysis of the atomic displacement before and after the interaction of a $12V$-SFT with the (a) asymmetric $\mathrm{\Sigma }11$ tilt, (b) CuNb KS1, and (c) ARB KS interfaces. Blue particles represent vacancies while purple describes interstitial-like particles before the interaction. Green particles represent vacancies and red describes interstitial-like particles after the interaction. These are identified via a lattice-reference method in which the structure is compared before and after the reaction. In panel (a) gray atoms belong to unknown structure and black to hcp. In panels (b) and (c) gray and black atoms are Cu and Nb, respectively, belonging to the interface. The maps in the insets show the vacancy-interface interaction energy with the pristine interface.

Figure 12

Single vacancies (brown) and vacancy clusters (blue) found from OKMC simulations considering vacancy clusters (SFTs) as (a) sessile or (b) glissile at 700 K and a dose rate of 5.5 ${10}^{-4}$ dpa/s after 1 s. Panel (c) shows the distribution of single vacancies and panel (d) shows the distribution of vacancies in clusters for both cases. L denotes the dimension perpendicular to the interfaces.