Crystal Structures and Mechanical Properties of Ca₂C at High Pressure

Abstract

Recently, a new high-pressure semiconductor phase of Ca₂C (space group Pnma) was successfully synthesized, it has a low-pressure metallic phase (space group C2/m). In this paper, a systematic investigation of the pressure-induced phase transition of Ca₂C is studied on the basis of first-principles calculations. The calculated enthalpy reveals that the phase transition which transforms from C2/m-Ca₂C to Pnma-Ca₂C occurs at 7.8 GPa, and it is a first-order phase transition with a volume drop of 26.7%. The calculated elastic constants show that C2/m-Ca₂C is mechanically unstable above 6.4 GPa, indicating that the structural phase transition is due to mechanical instability. Both of the two phases exhibit the elastic anisotropy. The semiconductivity of Pnma-Ca₂C and the metallicity of C2/m-Ca₂C have been demonstrated by the electronic band structure calculations. The quasi-direct band gap of Pnma-Ca₂C at 0 GPa is 0.86 eV. Furthermore, the detailed analysis of the total and partial density of states is performed to show the specific contribution to the Fermi level.

Keywords: Ca2C; first-principles calculations; pressure-induced phase transition.

Figure 1

Crystal structures of Ca₂C. (a) Pnma-Ca₂C; (b) C2/m-Ca₂C. The black and blue spheres represent C and Ca atoms, respectively.

Figure 2

Enthalpy (a) and volume (b) as a function of pressure. The black and red solid lines represent Pnma-Ca₂C and C2/m-Ca₂C, respectively.

Figure 3

Lattice parameters X/X₀ as a function of pressure. (a) Pnma-Ca₂C; (b) C2/m-Ca₂C.

Figure 4

Calculated ${\tilde{C}}_{44}{\tilde{C}}_{66}-C_{46}^2$ of C2/m-Ca₂C under different pressures.

Figure 5

Phonon spectra for (a) Pnma-Ca₂C at 0 GPa; (b) Pnma-Ca₂C at 100 GPa; (c) C2/m-Ca₂C at 0 GPa; (d) C2/m-Ca₂C at 6.4 GPa.

Figure 6

Elastic constants as a function of pressure. (a) Pnma-Ca₂C; (b) C2/m-Ca₂C.

Figure 7

2D representations of the Young’s modulus. (a) Pnma-Ca₂C at 0 GPa; (b) Pnma-Ca₂C at 100 GPa; (c) C2/m-Ca₂C at 0 and 6 GPa; (d) C2/m-Ca₂C at 6 GPa. The black, red and green lines represent the xy, xz and yz planes, respectively.

Figure 8

2D representations of Poisson’s ratio. (a) Pnma-Ca₂C at 0 GPa; (b) Pnma-Ca₂C at 100 GPa; (c) C2/m-Ca₂C at 0 GPa; (d) C2/m-Ca₂C at 6 GPa. The solid and dash lines represent the maximal and minimal positive values, respectively. The black, red and green lines represent the xy, xz and yz planes, respectively.

Figure 9

2D representations of shear modulus. (a) Pnma-Ca₂C at 0 GPa; (b) Pnma-Ca₂C at 100 GPa; (c) C2/m-Ca₂C at 0 GPa; (d) C2/m-Ca₂C at 6 GPa. The solid and dash lines represent the maximal and minimal positive values, respectively. The black, red and green lines represent the xy, xz and yz planes, respectively.

Figure 10

Electronic band structure and density of state of Pnma-Ca₂C (a) and C2/m-Ca₂C (b) at 0 GPa.