Initiation to the theoretical study of materials: DFT for C, Si, Ge and Sn

Abstract

The study of condensed matter is one of the main fields in modern Physics. A few years ago, was divided into two streams: "hard" condensed matter physics, which studies quantum properties of matter, and "soft" condensed matter physics which studies those properties of matter for which quantum mechanics plays no role. Central to this field is to understand how electrons and nuclei interact according to the wellestablished laws of electromagnetism and quantum mechanics, and try to explain their properties. The complexity of the computational calculus is insanely huge. Nowadays it is normal to understand this field as something collaborative between different groups of researchers in order to have access, not only to more human resources but also to hardware or software that allows in some way or another to reduce this computational cost. The ab initio theories and calculations try to access physical-mathematical routes that shorten these in an analytical way and also nourished by an empirical support to offer the best possible approximations. The present work will be focused in an introductory background of these ab initio calculations that will support our understanding of how they will applied to study different materials, in both diamond structures, cubic and hexagonal (called lonsdaleite) for C (Carbon), Si (Silicon), Ge (Germanium) and Sn (Tin). The program used will be VASP (Vienna ab initio Simulation Package). Convergence studies, Equations of States with Birch-Murnaghan approximation, Density of States, band structure and phonon frequencies will be studied. The results obtained are consistent with current published calculations and theories, thus confirming to the reproducibility and consistency of the results. Therefore, they will be compared with publications extracted from different sources (the most used one is Arxiv). The diamond structure appears in different materials. It has beautiful optical properties and a very high thermal conductivity (Carbon). Still, the hexagonal form of diamond (it was observed for the first time in meteorite craters [1]), could now be produced e.g. under shock compression experiments [2], and is significantly stiffer and stronger than regular gem diamonds. The understanding of the differences between them could give us a key for the next step in the discovering new materials.