We demonstrate quantitative determination of key structural parameters such as surface roughness, inter- and intralayer spacings, stacking order, and interlayer twist using a rudimentary transmission electron microscope. Combining electron diffraction and specimen tilt we probe Bragg rods in all three dimensions to identify multilayer structure with subangstrom precision across several 2D materials-including TMDs ( MoS 2, TaSe 2, TaS 2) and multilayer graphene. Discerning these structural order parameters is often difficult using real-space measurements however, we show that 2D materials have distinct, conspicuous three-dimensional (3D) structure in reciprocal space described by nearly infinite oscillating Bragg rods. For transition metal dichalcogenides (TMDs), bond coordination within a single van der Waals layer changes the out-of-plane symmetry that can cause metal-insulator transitions or emergent quantum behavior. The field of two-dimensional (2D) materials has expanded to multilayered systems in which electronic, optical, and mechanical properties change-often dramatically-with stacking order, thickness, twist, and interlayer spacing.
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