Direct Measurements of Surface Strain-Mediated Lateral Interactions between Adsorbates in Colloidal Heteroepitaxy

Surface strain can alter the dynamics of adsorbates, and often, the adsorbates themselves induce and interact via their surface strain fields. In epitaxy, such strain-mediated effects get further compounded when a misfit strain exists due to lattice mismatch between the growing film and substrate. Here, we carry out particle-resolved imaging of heteroepitaxial growth of multilayer colloidal films where the particles interact via a short-range attraction. Surprisingly, although the misfit strain relaxed systematically with film thickness, the adcolloid diffusivity was nonmonotonic. We show that this nonmonotonicity stems from the competition between the spatial extent of self-induced in-layer strain and the short interaction range. Importantly, we provide direct evidence for long-ranged strain-mediated interactions between adsorbates and show that it alters the growing film’s morphology.

Figure 1

(a) Film morphology for different misfit strain, $ϵ$, values with particle color representing the layer number (see color bar). For $ϵ\ge 5.5\%$, islands tended to dewet from the substrate and form hexagonal domains (circled region). (b) Average in-layer strain, ${ϵ}_{\text{layer}}$, with film thickness. ${ϵ}_{\text{layer}}$ for each layer was measured at a coverage $\mathrm{\Theta }={\mathrm{\Theta }}_{\text{Onset}}$, i.e., when island nucleation initiated in the layer above. The shaded region denotes pseudomorphic growth. (c) Nearest-neighbor bonds, colored according to legend, for $\mathrm{\Theta }$ below (left panel) and above (right panel) ${\mathrm{\Theta }}_{\text{Onset}}$ for $ϵ=4.5\%$. (d) Bond-length distribution, $P(\sigma )$, for square-coordinated particles for $ϵ=4.5\%$ and $ϵ=1\%$ at various $\mathrm{\Theta }$. The solid and dashed lines represent the equilibrium (${\sigma }_f$) and substrate lattice constant (${\sigma }_s$), respectively.

Figure 2

(a) Adcolloid diffusivity, $D$, on each layer for $ϵ=4.5\%$ and $ϵ=1\%$. (b) Particle strain, ${ϵ}_P$, in the layer beneath the adcolloid for the 1st, 2nd, and 3rd nearest-neighbor (NN) particles for $ϵ=4.5\%$. ${ϵ}_P$ is measured when the adcolloid is at a hollow site and the symbols represent the layer in which the adcolloid resides. (c) Diagrammatic representation of (b). Here, the grid colors represent the experimentally measured ${ϵ}_P$ (see color bar). Notice that the grid is maximally distorted from a square shape in the 2nd layer. The range of the adcolloid-induced strain field is largest here and results in a minimum in $D$. (d) and (f) show ${ϵ}_P$ in the first layer, for a pair of adcolloids separated by ${\sigma }_s$ above for $ϵ=4.5\%$ and $ϵ=1\%$, respectively. (e) and (g) show the probability $P_{\mathrm{hop}}$ for adcolloids to make a hop toward or away from each other for $ϵ=4.5\%$ and $ϵ=1\%$, respectively.

Figure 3

(a) and (b) show an island on the first layer for $ϵ=4.5\%$ and $ϵ=1\%$, respectively. The particles in the island are shown by dashed white circles. The part of the image containing the island also appears darker during imaging due to the presence of an additional layer of particles. The overlaid lines represent ${ϵ}_P$ in the first layer (see color bar). (d) and (e) show the residence time ${\tau }_R$ of adcolloids at hollow sites located at various distances $R/{\sigma }_s$ from the island edge for $ϵ=1\%$ and $ϵ=4.5\%$, respectively. ${\tau }_R$ is the duration that an adparticle center lies inside a square box of size $0.5{\sigma }_f$ centered at the hollow site [26]. See schematic shown in (c). (f) Island density $n$ versus $\mathrm{\Theta }$ for the two misfits.