First-principles investigation on elastic and thermodynamic properties of Pnnm-CN under high pressure

Abstract

The elastic anisotropy and thermodynamic properties of the recently synthesized Pnnm-CN have been investigated using first-principles calculations under high temperature and high pressure. The calculated equilibrium crystal parameters and normalized volume dependence of the resulting pressure agree with available experimental and theoretical results. Within the considered pressure range of 0-90 GPa, the dependences of the bulk modulus, Young's modulus, and shear modulus on the crystal orientation for Pnnm-CN have been systematically studied. The results show that the Pnnm-CN exhibits a well-pronounced elastic anisotropy. The incompressibility is largest along the c-axis. For tension or compression loading, the Pnnm-CN is stiffest along [001] and the most obedient along [100] direction. On the basis of the quasi-harmonic Debye model, we have explored the Debye temperature, heat capacity, thermal expansion coefficient, and Grüneisen parameters within the pressure range of 0-90 GPa and temperature range of 0-1600K.

FIG. 1.

Crystal structure of Pnnm-CN. The black and blue spheres represent C and N atoms, respectively.

FIG. 2.

The normalized parameters a/a₀, b/b₀, c/c₀, and V/V₀ as a function of pressure for Pnnm-CN.

FIG. 3.

The calculated elastic constants as a function of pressure for Pnnm-CN.

FIG. 4.

Three-dimensional surface depictions (a) and plane projections of the directional dependence of the Young’s modulus (b); Three-dimensional surface depictions (c) and plane projections of the directional dependence of the bulk modulus (d).

FIG. 5.

Orientation dependences of Young’s modulus (a) and shear modulus (b) for Pnnm-CN.

FIG. 6.

The calculated specific heat capacity at constant volume C_V and at constant pressure C_P as a function temperature for Pnnm-CN at different pressures: C_V contours (a), $C_V-T$ (b), C_P contours (c), $C_P-T$ (d).

FIG. 7.

Variation of the thermal expansion coefficient with pressure for Pnnm-CN at different temperatures (a). Variation of the thermal expansion coefficient with temperature for Pnnm-CN at different pressures (b).

FIG. 8.

Variation of the Grüneisen parameter with pressure for Pnnm-CN at different temperatures (a). Variation of the thermal expansion coefficient with temperature for Pnnm-CN at different pressures (b).