Modeling of Diffusivity for 2D Vacancy Nanopits and Comparison with 2D Adatom Nanoislands on Metal(100) Surfaces Including Analysis for Ag(100)

Abstract

Diffusion coefficients, DN, for 2D vacancy nanopits are compared with those for 2D homoepitaxial adatom nanoislands on metal(100) surfaces, focusing on the variation of DN with size, N. Here, Nis measured in missing atoms for pits and adatoms for islands. Analysis of DN is based on kinetic Monte Carlo simulations of a tailored stochastic lattice-gas model, where pit and island diffusion are mediated by periphery diffusion, i.e., by edge atom hopping. Precise determination of DNversus N for typical parameters reveals a cyclical variation with an overall decrease in magnitude for increasing moderate O(102) ≤ N ≤ O(103). Monotonic decay, DN ∼ N-β, is found for N ≥ O(102) with effective exponents, β = βeff, for both pits and islands, both well below the macroscopic value of βmacro = 3/2. DN values for vacancy pits are significantly lower (higher) than for adatom islands for moderate N in the case of low (high) kink rounding barrier. However, DN values for pits and islands slowly merge, and βeff → 3/2 for sufficiently large N. The latter feature is expected from continuum Langevin formulations appropriate for large sizes. We compare predictions from our model incorporating appropriate energetic parameters for Ag(100) with different sets of experimental data for diffusivity at 300 K, including assessment of βeff, for experimentally observed sizes N from ∼100 to ∼1000.ABSTRACT: Diffusion coefficients, DN, are compared for 2D vacancy nanopits with those for 2D homoepitaxial adatom nanoislands on metal(100) surfaces, focusing on the variation of DN with size, N. Here, N is measured in missing atoms for pits or adatoms for islands. Analysis of DN is based on Kinetic Monte Carlo simulations of a tailored stochastic lattice-gas model, where pit and island diffusion is mediated by edge atom hopping. Precise determination of DN versus N reveals cyclical variation with an overall decrease in magnitude for increasing moderate N ≤ O(10 2 ). Monotonic decay, DN ~ N -β , is found for N ≥ O(10 2 ) with effective exponents, β = βeff, for both pits and islands, both well below the macroscopic value of βmacro = 3/2. DN values for vacancy pits are significantly lower (higher) than for adatom islands in the case of low (high) kink rounding barrier. However, DN values for pits and islands slowly merge, and βeff → 3/2 for sufficiently large N. The latter feature is expected from continuum formulations appropriate for large sizes. We compare predictions from our model incorporating appropriate energetic parameters for Ag(100) with different sets of experimental data, including assessment of βeff, for experimentally observed sizes N from ~100 to ~1000.

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling

“…The IVA choice has been used to effectively and elucidate fundamental NC diffusion, reshaping, and sintering processes on (100) surfaces. [153][154][155][156] See Figure 12 and also Sec.5.2, 5.4 and 8.1.…”

“…The reason is that there are pathways for pit diffusion which avoid any corner or kink rounding. 167 Returning to analysis of experimental data, the ISU 14 and Bochum groups 342 have compared vacancy nanopit and Ag adatom island or NC diffusion for Ag(100), and both find similar D NC for the same N. It should be noted, however, that these studies are not fully consistent with the ORNL data in Figure 121. The ISU data have somewhat higher values for island diffusivity, and the Bochum data have much larger values.…”

“…With this target, the tailored model was shown to recover the proposed behavior upon choosing Ee  0.29 eV,   0.18 eV,   0.27 eV, and  = 10 13 /s. 156 Finally, we remark that experimental data is available for diffusivity of vacancy pits on Cu (111) and Ag(111), 243,283 (111). Perhaps the optimal 2D example of Ostwald Ripening (OR), for which there exists detailed information on the evolution of the island distribution, is provided by STM studies of the coarsening of Ag islands on an Ag(111) surface.…”

“…166 Next, we briefly describe analysis of the diffusion of singleatom deep vacancy nanopits on metal(100) surfaces using the same tailored model as just applied for adatom cluster diffusion. 167 Results for δ KES = 0 are shown in Figure 125. In this case with δ KES = 0, D NC for pits is lower than for adatom clusters or islands of the same size.…”

Nanoscale modification of silicon and germanium surfaces exposed to low-energy helium plasma

“…As no bubble formation is observed in silicon or germanium, vacancies are likely to eventually recombine with the surface as well where they will preferentially drive surface pit formation 26 , enhancing surface roughening further. Germanium is an unusual case as its vacancy diffusivity is exceptionally high 14 : roughly 2 × 10 −7 cm 2 /s at 240 °C, similar to that of the self-diffusion of a body-centered cubic metal at its melting point.…”