Surface Roughening and Unstable Neck Formation in Faceted Particles: II, Mathematical Modeling

Abstract

Unstable neck formation between two isolated particles was analyzed by considering the effects of both faceted and rounded (i.e., "atomically rough") surfaces. Mathematical descriptions of both neck growth and rupture are developed here. Calculations conducted with these formulations can explain the neck instability observed by Rankin and Boatner. The analysis and the experimental data suggest that the energy barrier associated with forming a new atomic layer on top of a faceted surface can restrict the shape evolution of a crystalline particle, even at moderately high temperatures. The analysis also indicates that this energy barrier can be overcome when the positive curvature which initially exists at a facet/rough surface boundary reverses as a result of neck growth. This latter effect offers an explanation for neck rupture which is consistent with the experimental results. In addition to providing an explanation for this phenomenon, the analyses presented here also demonstrate that surface phase boundaries and step energy barriers can have a significant effect on microstructure evolution during solid-state sintering.

Experimental Evidence for the Development of Bimodal Grain Size Distributions by the Nucleation‐Limited Coarsening Mechanism

“…In the absence of a persistent source of these steps (such as a screw dislocation), a terrace must be nucleated and there will be an energy barrier for this process. The nucleation energy barrier has also been cited as influencing the initial stages of sintering 15,16 . The presence of a barrier during coarsening is consistent with the conventional theory for the growth of crystals from a vapor, a solution, or from a supercooled melt 17 .…”

Computational Modeling of Nanoparticle Coalescence

“…Mc-Carthy and Brown dissected the equilibration of a partially coalesced system of faceted clusters into three steps, namely the dissociation of atoms from existing atomic layers, their diffusion across and between facets, and the nucleation of new germs, [49] in agreement with previous studies that assumed that necking required (and its rate depended on) new germs grown on facets. [81,82] At any rate, all atomistic simulation results agree on the much lower rate of this diffusion-driven progression compared with the previous stage of plastic deformation; an example is shown in Figure 8, juxtaposing the evolution of the coalescence process obtained by atomistic simulations of Lewis et al and the continuous numerical solution by Nichols. [81,82] At any rate, all atomistic simulation results agree on the much lower rate of this diffusion-driven progression compared with the previous stage of plastic deformation; an example is shown in Figure 8, juxtaposing the evolution of the coalescence process obtained by atomistic simulations of Lewis et al and the continuous numerical solution by Nichols.…”

Step‐Energy Barriers and Particle Shape Changes during Coarsening

“…(7) at small values of : 2 2! ͬ ϩ higher-order terms (14) As noted in discussing Eq. (12), the first term on the right-hand side of Eq.…”