Study of thermodynamic properties changes of Nickel Oxide by DFT method and Romberg integration up to 5000 °C and 100 GPa

Abstract

This paper aims to illustrate how Romberg's numerical integration is applied in calculating the values of internal energy, free energy, entropy and heat capacity at constant volume. Which is considered one of the important parameters of thermodynamic properties, and it is the only one that depends on integrations in its calculation. The temperature changes from zero to 5000 °C, while the pressure changes between zero and 100 GPa. The application was made to nickel oxide which remains in its cubic phase in this pressure range, and the Debye temperature values for it are determined by the CASTEP program which including the DFT method exactly by GGA approximation via the PBEsol function. We found that the Debye temperature decreases with increasing pressure and its value at absolute zero is slightly consistent with previous studies, confirming the validity of these results. However, we could not compare with the thermodynamic parameters, which we found to also decrease with increasing pressure, except for the values ​​of internal energy, heat capacity at constant volume and entropy values ​​for low temperatures. Conversely, this exception is adopted for increasing temperature, with most parameters showing an increase with increasing temperature.