Abstract: Crystal is a fundamental and important concept in solid state physics. But the reason why different element crystals present different crystal types, such as face centered cubic (fcc), body centered cubic (bcc), hexagonal dense packing (hcp), and even simple cubic structure (sc), is not explained in the course. In this paper, the single point energy of metal crystals such as polonium (Po), tungsten (W), aluminum (Al) and magnesium (Mg) is calculated by using the density functional theory and the first principle software quantum Espresso. The energy curves varying with the lattice constant under different crystal structures are obtained. The theoretical lattice structure of each metal crystal is discussed, and the problem of different crystal types of different solid crystals is explained.

Key words:  solid state physics, metal crystal, first principle theory, quantum Espresso