MATLAB Code Implementation for Visualizing Graphene Structure

Visualizing graphene structure is a crucial step in understanding its unique physical properties. Graphene consists of a single layer of carbon atoms arranged in a hexagonal lattice pattern, where each carbon atom forms covalent bonds with three neighboring atoms. MATLAB provides powerful matrix operations and graphical plotting capabilities that enable effective visualization of this atomic structure. First, determine the geometric parameters of the graphene lattice. The hexagonal lattice can be described using two basis vectors, with the side length of each hexagon (carbon-carbon bond length) approximately 0.142 nanometers. To simplify the plotting process, create a 2D coordinate system where carbon atom positions are generated through linear combinations of the basis vectors. In MATLAB implementation, this typically involves defining lattice vectors and calculating atomic positions using matrix multiplication operations. In MATLAB, carbon atom coordinates can be generated through loops or matrix operations. For example, start by generating vertex coordinates for a single hexagon unit, then use translation operations to replicate the hexagonal unit cell, forming a periodic graphene lattice. To realistically simulate graphene's infinite structure while maintaining computational efficiency, set a finite drawing range and clearly mark the fundamental lattice unit. A common approach is to use nested loops or meshgrid functions to generate the hexagonal pattern across the specified domain. During plotting, utilize MATLAB's graphical functions such as `plot` or `scatter` to display carbon atom positions, and connect neighboring atoms with line segments to simulate covalent bonds. For optimal visual representation, adjust point size and color using `scatter` parameters, and control line thickness and style through `plot` property settings. The `line` function can be employed to draw bonds between coordinated atoms based on their adjacency matrix. Additionally, use MATLAB's graphical interface tools like `figure` and `axis` to set appropriate coordinate ranges and labels, clearly demonstrating graphene's hexagonal symmetry. Through `axis equal` command, maintain proportional scaling to preserve the geometric accuracy of the lattice structure. This implementation not only provides intuitive understanding of graphene's atomic arrangement but also establishes a foundation for subsequent analysis of its physical properties. The code typically involves coordinate generation algorithms, neighbor identification routines, and customizable visualization parameters for research and educational purposes.