Study of Structural and Electronic Properties of Sodium and Potassium

Abstract

We optimize lattice parameter and identify the nature and values of band gap of Sodium and Potassium by using quantum espresso. This work includes the general introduction on crystal structure and different models that work in the lattice constant and lattice dynamic. We also briefly include various theoretical details such as Born-Oppenheimer Approximation, Hartree-Fock Approximation, Density Functional Theory, Kohn-Sham approach, Local Density approximation, Generalized Gradient Approximation, and pseudo- potential. Finally, we discussed the fundamentals of Quantum Espresso computational program with the result and discussion on electronic properties, kinetic energy cut-off, lattice parameter, band gap, density of state and partial density of state of Sodium and Potassium. We optimize lattice parameter and identify the nature and values of band gap of Sodium and Potassium structure. Optimized value of the lattice constant, kinetic energy (cut off energy), K-point grid and degauss of Sodium is obtained as 7.91 Bohr ,80 Ry,12×12×12 and 0.005 respectively. Similarly, Optimized value of the lattice constant, kinetic energy (cut off energy), K-point grid and degauss of Potassium is obtained as 9.96 Bohr ,85 Ry,12×12×12 and 0.004 respectively. By optimizing lattice parameter, we calculate band gap and nature of element. We found that there is no band gap between valance and conduction band of both Sodium and Potassium. Also, from DOS graph, we found that there are no significant changes in peaks so, we conclude that they form ionic bonding with other element. We also calculate percentage error of lattice constant which is 2.34% for Sodium and 0.99% for Potassium. We used norm-conserving pseudo potentials; self-consistent calculations employed Density Functional Theory (DFT) under Generalized Gradient Approximation (GGA) by using Quantum ESPRESSO package.