Physics Commons^™

Atom-Based Geometrical Fingerprinting Of Conformal Two-Dimensional Materials, Mehrshad Mehboudi

Graduate Theses and Dissertations

The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated.

The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which …