SATURACION TEMPERATURA DE SATURACION ( °C )

As previously mentioned, slip in a <110> oriented nanowire will occur on one of two degenerate slip planes (Figure 8.5c). The other two that make up the four slip planes have zero resolved shear stress and do not contribute to plastic deformation (Figure 5b). If we again limit ourselves to consider specifically a [011] nanowire and the (111) slip plane, the three partial dislocations on this slip plane are again the !_![112], !_![121] and !_![211]. The leading and trailing partial dislocations are reversed from the <100> nanowires: the !_![112] is the trailing partial in tension and leading partial in compression while the !_![121] and !_![211] are the leading partials in tension and trailing partials in compression.

Figure 8.8 The geometry of slip in (110) nanowires. (a) The {111} slip plane of a square nanowire with {100} × {110} side surfaces showing two potential source sites in compression. While the two sites appear equivalent, the energy barriers are different if the Burgers vectors are the same. (b) The actual nucleation site in the nanowire under

compression as predicted by our atomistic simulations. (c) The (110) nanowire with a circular cross-section with two potential nucleation sites in compression. (d) The actual nucleation site as predicted by our atomistic simulations. (e) The {111} slip plane of a square nanowire with {100} side surfaces showing two potential source sites in tension. (f) The actual nucleation site in the nanowire under tension as predicted by our atomistic simulations. (g) The (110) nanowire with a circular cross-section with one potential nucleation sites in tension. (h) The actual nucleation site as predicted by our atomistic simulations. (i) The (110) nanowire with a rhombic cross section illustrating the two potential nucleation sites and (j) the actual nucleation site as predicted by our atomistic simulations. Note that all of the

dislocations shown here are super critical in size, but are used to make the figures clearer.

Figure 8.8 shows a geometric representation of nucleation sites compared against the actual nucleation sites in the <110> nanowires. We observe again that the nucleation site is the one that appears to reduce line length as well as maintain an orientation close to screw. This agrees with the trends observed in <100> nanowires. As an example, the rhombic <110> nanowire in tension (Figure 8.8i,j) shows nucleation that looks very similar to the square nanowire in compression, where the two Burgers vectors and Schmid factors are the same and the geometries are similar. The circular <110> nanowires in tension and compression show the similar profiles to the circular (100) nanowires with the opposite loading direction. The slight differences between the shape of the <110> compression and <100> compression may have to do with the eccentricity of the ellipsoidal slip planes.

Figure 8.9 The activation energy of dislocation nucleation in (110) gold nanowires for (a) compression and (b) tension. The activation volume, determined from the derivative of the curve fit, is shown in (c) for compression and (d) for tension. The circles, squares, and diamonds are the atomistic data points for circular and square and rhombic prisms, respectively.

The <110> rhombic nanowire data for compression is not shown although energy barrier calculations were performed. This is partially due to the nature of the nucleation showing conflicting results. For stresses ~ 6 GPa (energy barrier of 1.0 eV), our results show a stable dislocation nucleating from the free surface. However, higher stress calculations actually show homogeneous

nucleation in the center of the nanowire, which agree with our low temperature (0.01 K) simulations, although these dislocations nucleate while the nanowire is undergoing an elastic instability. This is a strange result at first, however unusual behavior of <110> nanowires with {111} side surfaces in compression was reported before by Park et al. [122]. They observed in gold (using the same potential), nickel, and copper that line defects did not nucleate in their simulations. While our results are different, showing line defects nucleating, the unusual nature of our results suggests that reporting a single energy barrier curve would be inappropriate. In order to fully explore this phenomenon a range of mechanisms would need to be explored through the string method to and a set of energy barrier curves would need to be reported.

Figure 8.9 shows the energy barrier curves and activation volume curves or <110> nanowires in tension and compression. The Schmid factors for the leading partials in compression are about half that of the leading partials in tension. We note that this signature appears again in the energy barrier curves with the compression barriers being larger than those in tension. Furthermore, the activation volumes in compression are much lower than those in tension with the compression activation volume is less than 4𝑏! _{while the tension data has values well above 10𝑏}!_{. These results also support the}

notion that the square prisms are weaker than the circular prisms. The circular prism and rhombic prism show very similar energy barrier curves converging upon one another at high stresses.

The energy barrier calculations performed here show a complete picture of dislocation nucleation. From the reaction pathways we see that dislocations prefer to nucleate in the screw orientation in order to reduce their line energy. The energy barrier curves show that square prisms are generally weaker than circular prisms, which we hypothesize primarily occurs from the reduction in line length from corner nucleation. The computed activation volumes are small, confirming that nucleation is both temperature and strain rate dependent. A comparison of the fitted athermal strength, 𝜎_!, shows very good correlation with the athermal strength computed from molecular statics,

𝜎_!"!, except in the case of <110> where buckling is observed in molecular statics rather than spontaneous dislocation nucleation. In the next section, we will use a pure continuum model and repeat our calculations and confirm the role of line energy in controlling nucleation. In Section 4, the energy barrier calculations will be used to predict strengths in gold nanowires.