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Two-dimensional crystals such as graphene and transition metal dichalcogenides have emerged as a new class of materials. They serve as rich playgrounds for two-dimensional physics but also have great potential for a wide range of applications due to their exceptional tunability via external influences such as electric fields, light, chemical adsorbates, defects, and stress. This dissertation aims to understand, as a fundamental step toward their application, the response of two-dimensional crystals to such external perturbations imposed by supporting substrates.

First, the mechanical response of graphene supported on corrugated substrates is studied. I find that the structural evolution of graphene depends on the roughness of the substrate and the graphene thickness. On SiO2 substrates decorated with a low-density of SiO2 nanoparticles, adhesion dominates graphene elasticity and, hence, graphene conforms to the substrate. With increasing nanoparticle density, however, the elastic stretching energy is reduced by the formation of wrinkles. As the graphene membrane is made thicker, graphene becomes stiffer and delaminates from the substrate.

Second, the effect of substrates on chemical reactivity of graphene is probed. Single-layer graphene on low charge-trap density boron nitride is not etched and shows little doping after oxygen treatment, in sharp contrast with oxidation under similar conditions of graphene on high charge-trap density SiO2 and mica. Furthermore, bilayer graphene shows reduced reactivity compared to single-layer graphene regardless of its substrate-induced roughness. Together the observations indicate that graphene's reactivity is predominantly controlled by charge- inhomogeneity-induced potential fluctuations rather than by surface roughness.

Lastly, the oxidative reactivity of atomically thin molybdenum disulfide (MoS2) on SiO2 is studied. MoS2 is etched by oxygen treatment. However, unlike graphene on SiO2, the density of etch pits barely depends on MoS2 thickness, oxidation time, oxidation temperature, but varies significantly from sample to sample. The observations suggest that the oxidative etching of atomically thin MoS2 is initiated at native defect sites on the basal-plane surface rather than activated by substrate effects such as charged impurities and surface roughness.

The findings provide insight into the mechanical and chemical properties of two-dimensional crystals and may have important implications for their applications.