Fig. 3: Mechanics of atomically thin domes.
From: Nanoscale engineering of non-uniform biaxially strained domes
a hm versus R of different spontaneously formed MX2 domes. hm/R provides the biaxial tensile strain at the dome apex εm by the inset equation81. b Height profile comparison between an MoS2 dome and FEA. R and hm are 3.76 µm and 618 nm, respectively (left axis is the height coordinate). Strain tensor along the radial (εr), circumferential (εt), and perpendicular (εz) directions calculated from finite element analysis (FEA) (right axis)81. c Numerical calculations of the constant q versus the experimentally obtained region of q depicted by the shaded areas, which highlight the range of aspect ratios measured experimentally over many 2D material dome samples88. d Normalised centre strain comparison between FEA, analytical and experimentally determined strain from Raman experiments88. εr and εϑ refer to εrr and εϑϑ, given by Eqs. (3) and (4), respectively. e Aspect ratio of triangular footprint domes90. f Aspect ratio of pyramidal footprint domes90. g Dome pressure as a function of R for 1-3 L domes. The average hm/R values of 1 − 3 L domes are 0.18, 0.17 and 0.16, respectively97. h Stiffness as a function of R for 1–3 L domes97. i Stable plate to membrane transition mechanics of domes induced by SEM irradiation98. j Engineered domes using a mask with S = 1 μm. The strict boundary condition enable domes to increase in hm/R, enabling biaxial strains up to ~10% at the centre of the dome82. Figures a and b adapted from Copyright (2019) Wiley. Used with permission from (Tedeschi. D. et al., Controlled Micro/Nanodome Formation in Proton-Irradiated Bulk Transition-Metal Dichalcogenides, Advanced Materials). Figures c and d adapted from reprinted (figure) with permission from Blundo, Elena and Yildirim, Tanju and Pettinari, Giorgio and Polimeni, Antonio, Phys. Rev. Lett., 127, 046101, 2021.] Copyright (2021) by the American Physical Society. Figure j adapted from Copyright (2020) Wiley. Used with permission from (Blundo. E. et al., Engineered Creation of Periodic Giant, Nonuniform Strains in MoS2 Monolayers, Advanced Materials Interfaces).
