*3.1. Void Nucleation Process*

In our simulations, we generally observed the sequence of events depicted in Figure 2. At the start of the load holding step there was no evidence of cracking or voiding at the particle interface. After some time, one or more clusters of atoms began exhibiting relatively large atomic volumes, indicating the nucleation of a crack with the size of a small vacancy cluster. For example, in Figure 2a we show atoms in blue whose atomic volume exceeds 30 Å<sup>3</sup> based on Voronoi analysis. For reference, the atomic volume of aluminum is 16.7 Å3. The specific mechanism by which this vacancy clustered appeared could not be determined. Over time this crack grew, leading to a larger patch of atoms with volumes exceeding 30 Å<sup>3</sup> as shown in Figure 2b. Importantly, this crack growth was not accompanied by any dislocation activity. Instead, the crack grew steadily in time; in the Discussion we demonstrate that this delamination rate is governed by the lattice trapping phenomenon [42], and hence refer to this as *lattice-trapped delamination*. Eventually, once the crack reached a critical size, Shockley partial dislocations nucleated at the tip of the crack approximately in the plane of the crack, as shown in Figure 2c. These dislocations then rapidly glided away from the particle into the bulk and began to multiply, joined by additional dislocations nucleating from the crack tip. The crack growth rate increased rapidly upon appearance of the dislocations, leading to total delamination of the particle from the matrix. We call this process *dislocation-mediated delamination*.

**Figure 2.** Simulation snapshots from a simulation with T = 400 K and *σ<sup>H</sup>* = 6.0 GPa. Blue atoms are associated with a crack (have an atomic volume > 30 Å3). (**a**) Initial appearance of a small crack involving a few atoms at t = 37 ps (relative to the start of the holding stage). (**b**) Subsequent growth of the crack via lattice-trapped delamination at t = 105 ps. (**c**) Initial appearance of dislocations at the crack tips at t = 126 ps. (**d**) Rapid crack growth via dislocation-mediated delamination at t = 139 ps. Green lines are Shockley-Read partial dislocations. Red atoms are associated with stacking faults.

Figure 3 shows atomic displacements associated with the two delamination modes. Figure 3a shows the atomic displacement vectors as black arrows over an 18 ps time period from the snapshot in Figure 2b to the moment just before dislocation nucleation Figure 2c. As shown, most of the crack growth is accommodated by displacements of atoms at the crack tip along the circumference of the particle. These displacements under lattice-trapped delamination are rather incoherent, in the sense that their direction and magnitude vary along the crack front in an uncoordinated manner. For example, several atoms experience large displacements while their immediate neighbors do not displace much at all (see yellow circled atoms). Displacements associated with dislocation-mediated crack growth over a 2 ps time period between the snapshots shown in Figure 2c,d are shown in Figure 3b. Once again, the displacements largely occur at the crack tip and in the circumferential direction, however these displacements are more coordinated in their direction and magnitude. These displacements appear to be due to nucleation and

 (**a**) (**b**)

glide of the dislocations visible in the figure, i.e., they are generally aligned with the Burgers vectors.

**Figure 3.** Snapshots from the same simulation as Figure 2 showing atomic displacements (black arrows) associated with (**a**) lattice-trapped delamination over an 18 ps time window and (**b**) dislocation-mediated delamination during a 2 ps time window. Blue atoms are associated with a crack (have an atomic volume > 30 Å3). Green lines are Shockley-Read partial dislocations. Red atoms are associated with stacking faults. Yellow circles denote atoms whose atomic trajectories differ significantly from their immediate neighbors.

To determine whether there were preferential nucleation sites on the particle's surface, we extracted the approximate crack nucleation location from 40 simulations and plot these locations in Figure 4 as a point cloud projected onto the *x*-*z* plane. This figure shows that while there may be a slight preference for nucleation at the negative *z*-axis pole of the precipitate (since there is a small cluster there), nucleation was also common at other points around the surface. Similarly, there is a lack of data points at the positive *z*-axis pole, indicating nucleation there is unfavorable. These results imply that our boundary conditions, simulation cell size, and precipitate orientation did not significantly influence the simulation behaviors (i.e., they did not introduce strong preferential sites).

**Figure 4.** Approximate crack nucleation locations projected onto the *x*-*z* plane from 40 simulations with various stresses and temperatures.

To assess the delamination behavior in the absence of thermal fluctuations, we performed molecular statics simulations of hydrostatic straining. We progressively increased the hydrostatic strain of the box by increasing the volume in 0.003% increments and minimizing the energy of the system after each strain increment. Each minimization step iterated until the change in energy during a minimization step was less than 10−6% or the norm of the global force vector was less than 10−<sup>8</sup> eV/Å. The resulting stress-strain curve is shown in Figure 5. We observe that at a hydrostatic stress of around 10 GPa, the particle catastrophically delaminates from the matrix. Hence, 10 GPa can be regarded as the athermal critical stress for void nucleation. The first peak in Figure 5 corresponds to the nucleation of dislocations at the poles of the particle along the *z*-axis. The subsequent peaks correspond to nucleation of dislocations around the entire circumference of the particle. Hence, it seems that athermal void nucleation is governed by the athermal nucleation of dislocations.

**Figure 5.** Hydrostatic stress-strain curve from a molecular statics simulation of delamination at *T* = 0 K. The peak stress is the stress required to delaminate the particle without the aid of thermal fluctuations.

To get information about the crack growth, we estimate the crack volume as *Vcrack*(*t*) = *V*(*t*) − *V*0, where *V*(*t*) is the volume of the simulation cell at time *t* and *V*<sup>0</sup> is the volume at the start of the holding phase. In Figure 6 we show a few examples of how the crack volume evolves over time during the load holding phase. In some cases, there appears to be an "incubation period" where the volume does not increase at all, followed by a gradual increase over time indicating the nucleation and growth of a crack. This gradual increase corresponds to the lattice-trapped delamination mode. In other cases, the volume appears to increase from the start of the load holding phase, with no obvious incubation period. In most cases it was difficult to unambiguously identify a clear "nucleation" event which correlated with a local increase in atomic volume at the void's surface. For this reason, we were unable to analyze any sort of "nucleation" rate directly from the incubation time. Regardless, lattice-trapped delamination was always observed in our simulations. We also mark in Figure 6 the time where the first dislocation nucleated. Upon nucleation of one or more dislocations, the system volume increases precipitously as the crack growth rate accelerates to complete delamination.

**Figure 6.** Crack volume as a function of time for simulations with T = 400 K and *σ<sup>H</sup>* = 6.0 GPa, each with a different random seed for atomic velocity initialization. Dashed lines denote the lattice-trapped delamination rates and circles mark the appearance of a dislocation.
