Pippard relations for cubic gauche nitrogen

Abstract

The Pippard relations (C_P vs. a_P and a_P vs. k_T) are examined at various temperatures up to 1200 K at zero pressure (P = 0) for the cubic gauche nitrogen. The specific heat (C_P) is related to the thermal expansion (a_P) and the a_P is also related to the isothermal compressibility (k_T) as the Pippard relations for this solid structure. For those relations, experimental data are used from the literature. It is found that the variation of the C_P with the a_P and a_P with the k_T is linear. Using the linear relations dP/dT is predicted, which can be compared with the experimental measurements in the P – T phase diagram of cubic gauche nitrogen.

Keywords

• Pippard relations,Cubic gauche nitrogen

References

1. [1] Schuch AF, Mills RI. Crystal structures of the three modifications of nitrogen 14 and nitrogen 15 at high pressure. J Chem Phys 1970; 52: 6000.
2. [2] Lesar R, Ekberg S, Jones L, Mills R. Raman spectroscopy of solid nitrogen up to 374 kbar. Solid State Commun 1979; 32: 131.
3. [3] Mills RL, Olinger B, Cromer DT. Structures and phase diagrams of N2and CO to 13 GPa by X-ray diffraction. J Chem Phys 1986; 84: 2837.
4. [4] Belak J, Lesar R, Etters RD. Calculated thermodynamic properties and phase transitions of solid N2 at temperatures 0≤T≤300 K and pressures 0≤P≤100 GPa. J Chem Phys 1990; 92: 5430.
5. [5] Schneider H, Hafner W, Wokaun A, Olijnyk H. Room temperature Raman scattering studies of external and internal modes of solid nitrogen at pressures 8≤P≤54 GPa. J Chem Phys 1992; 96: 8046.
6. [6] Gregoryanz E, Goncharov AF, Hemley RJ, Mao HK, Somayazulu M, Shen G. Raman, infrared and X-ray evidence for new phases of nitrogen at high pressures and temperatures. Phys Rev B 2002; 66: 224108.
7. [7] Mukherjee GD, Boehler R. High-pressure melting curve of nitrogen and the liquid-liquid phase transition. Phys Rev Lett 2007; 99: 225701.
8. [8] McMahan AK, Lesar R. Pressure dissociation of solid nitrogen under 1Mbar. Phys Rev Lett 1985; 54: 1929.

9. [9] Gregoryanz E, Goncharov AF, Hemley RJ, Mao HK. High pressure amorphous nitrogen. Phys Rev B 2001; 64: 052103.
10. [10] Goncharov AF, Gregoryanz E, Mao HK, Liu Z, Hemley RJ. Optical evidence for a nonmolecular phase of nitrogen above 150 GPa. Phys Rev Lett 2000; 85: 1262.
11. [11] Mailhiot C, Yang LH, McMahan AK. Polymeric nitrogen. PhysRev B 1992; 46: 14419.
12. [12] Eremets MI, Gavriliuk AG, Trojan IA, Dzivenko DA, Boehler R. Single-bonded cubic form of nitrogen. Nature Mater 2004; 3: 558.
13. [13] Eremets MI, Gavriliuk AG, Trojan IA. Single –crystalline polymeric nitrogen. App Phys Lett 2007; 90: 171904.
14. [14] Martin RM, Needs RJ. Theoretical study of the molecular-to-non molecular transformation of nitrogen at high pressures. Phys Rev B 1986; 34: 5082.
15. [15] Caracas R. Raman spectra and lattice dynamics of cubic gauche nitrogen. J Chem Phys 2007; 127: 144510.
16. [16] Pippard AB. The Elements of Classical Thermodynamics, Cambridge University Press, New York, 1957.
17. [17] Caracas R, Hemley RJ. New structures of dense nitrogen: path ways to the polymeric phase. Chem Phys Lett 2007; 442: 65.
18. [18] Nordlund K, Krasheninnikov A, Juslin N, Nord J, Albe K. Structure and stability of non-molecular nitrogen at ambient pressure. Europhys Lett 2004; 65: 400.
19. [19] Zhang T, Zhang S, Chen Q, Pheng LM. Metastability of single-bonded cubic gauche structure of N under ambient pressure. Phys Rev B 2006; 73: 094105.
20. [20] Yu HL, Yang GW, Yan XH, Xiao Y, Mao YL, Yang YR, Cheng MX. First principles calculations of the single-bonded cubic phase of nitrogen. Phys Rev B 2006; 73: 012101.