Direct Transformation of Vacancy Voids to Stacking Fault Tetrahedra

Defect accumulation is the principal factor leading to the swelling and embrittlement of materials during irradiation. It is commonly assumed that, once defect clusters nucleate, their structure remains essentially constant while they grow in size. Here, we describe a new mechanism, discovered during accelerated molecular dynamics simulations of vacancy clusters in fcc metals, that involves the direct transformation of a vacancy void to a stacking fault tetrahedron (SFT) through a series of 3D structures. This mechanism is in contrast with the collapse to a 2D Frank loop which then transforms to an SFT. The kinetics of this mechanism are characterized by an extremely large rate prefactor, tens of orders of magnitude larger than is typical of atomic processes in fcc metals.

Figure 1

Inset: The 20-vacancy void in Cu. In this display convention, red (or gray) spheres are vacancies. Notice the extra vacancy (labeled V) near one of the vertex sites (labeled C). Main figure: MEPs for the transformation of a 20-vacancy void to an SFT from 12 different MD simulations. The path in bold is analyzed in detail in the text; the others are shown for comparison. The hyperdistance of the reaction coordinate is the sum of the scalar distance all atoms move from one image to the next and has been shifted so that the highest energy saddle of each path is at 0. The circles and triangles represent the beginning and the end of each path.

Figure 2

MEP for the constant-volume transformation of a 45-vacancy void to an SFT. The inset figures are minima from the parallel-replica simulation showing the structure of the vacancy cluster as the transformation evolves [red (or gray) spheres are vacancies and blue (or dark gray) spheres interstitials, relative to an initial fcc reference structure]. The open circles are estimates of the free energy along the path.

Figure 3

SFT structures resulting from the transformation of a 45-vacancy void. (a) is the SFT from the pathway shown in Fig. 2, which still contains a small void of 9 vacancies, shown in (b) by the larger dark spheres. (c) is a nearly perfect SFT formed at $T=500\mathrm{K}$ (one vacancy is trapped in the interior). (d) is from a $T=600\mathrm{K}$ simulation; the void transforms into two smaller SFTs sharing an edge.

Figure 4

Stability of voids relative to SFTs as a function of vacancy cluster size for a number of fcc metals, calculated with EAM potentials. Except for small magic void sizes, SFTs are strongly preferred in Pd, Ni, Cu, and Ag. Voids are favored at small cluster size for Au and especially Pt.