Equation of state of nitrogen (N2) at high pressures and high temperatures: Molecular dynamics simulation

Nitrogen Dissolution in Liquid Ga and Fe: Comprehensive Ab Initio Analysis, Relevance for Crystallization of GaN

The dissolution of molecular nitrogen in Ga and Fe was investigated by ab initio calculations and some complementary experiments. It was found that the N bonding inside these solvents is fundamentally different. For Ga, it is between Ga4s and Ga4p and N2p states whereas for Fe this is by N2p to Fe4s, Fe4p and Fe3d states. Accordingly, the energy of dissolution of N2 for arbitrarily chosen starting atomic configurations was 0.535 eV/mol and -0.299 eV/mol for Ga and Fe, respectively. For configurations optimized with molecular dynamics, the difference between the corresponding energy values, 1.107 eV/mol and 0.003 eV/mol, was similarly large. Full thermodynamic analysis of chemical potential was made employing entropy-derived terms in a Debye picture. The entropy-dependent terms were obtained via a normal conditions path to avoid singularity of ideal gas entropy at zero K. Nitrogen solubility as a function of temperature and N2 pressure was evaluated, being much higher for Fe than for Ga. For T=1800 K and p=104 bar, the N concentration in Ga was 3×10-3 at. fr. whereas for Fe, it was 9×10-2 at. fr. in very good agreement with experimental data. It indicates that liquid Fe could be a prospective solvent for GaN crystallization from metallic solutions.

Determination of shear viscosity of molecular nitrogen (N2): molecular dynamic hard rotor methodology and the results

Determination of shear viscosity of molecular nitrogen (N(2)) by molecular dynamics (MD) in the high density range needs explicit incorporation of the rotational motion and therefore precise knowledge of angular dependence of N(2)-N(2) intermolecular potential. Newly designed Couette flow nonequilibrium molecular dynamic (NEMD) simulation procedure employs corrugated moving boundary, coupling the moving walls to translational and rotational motion exactly. Low density data on nitrogen viscosity show good agreement between MD data and experiment, confirming the radial dependence of the potential derived from quantum mechanical (QM) high precision calculations (coupled-cluster singles-and-doubles with a perturbative triples corrections [CCSD(T)]). Additionally, the angular dependence of the potential is verified using shear viscosity data for high density region, obtained from newly developed molecular dynamics (MD) simulations. It was demonstrated that the corrugated wall flow simulations provide results that are independent of the details of wall potential, fulfilling a basic requirement for application of MD simulations. These results are in good agreement with the equilibrium molecular dynamics (EMD) viscosity, derived from the Green-Kubo formula. Derived analytical dependence of the shear viscosity on the density and temperature shows that the MD data are in good agreement with experiment. Thus, MD simulations indicate that the CCSD(T) potential angular form is sufficiently precise for determination of the viscosity in a wide range of temperature and pressure.

Molecular nitrogen-N2 properties: The intermolecular potential and the equation of state

Quantum mechanical (QM) high precision calculations were used to determine N(2)-N(2) intermolecular interaction potential. Using QM numerical data the anisotropic potential energy surface was obtained for all orientations of the pair of the nitrogen molecules in the rotation invariant form. The new N(2)-N(2) potential is in reasonably good agreement with the scaled potential obtained by van der Avoird et al. using the results of Hartree-Fock calculations [J. Chem. Phys. 84, 1629 (1986)]. The molecular dynamics (MD) of the N(2) molecules has been used to determine nitrogen equation of state. The classical motion of N(2) molecules was integrated in rigid rotor approximation, i.e., it accounted only translational and rotational degrees of freedom. Fincham [Mol. Simul. 11, 79 (1993)] algorithm was shown to be superior in terms of precision and energy stability to other algorithms, including Singer [Mol. Phys. 33, 1757 (1977)], fifth order predictor-corrector, or Runge-Kutta, and was therefore used in the MD modeling of the nitrogen pressure [S. Krukowski and P. Strak, J. Chem. Phys. 124, 134501 (2006)]. Nitrogen equation of state at pressures up to 30 GPa (300 kbars) and temperatures from the room temperature to 2000 K was obtained using MD simulation results. Results of MD simulations are in very good agreement (the error below 1%) with the experimental data on nitrogen equation of state at pressures below 1 GPa (10 kbars) for temperatures below 1800 K [R. T. Jacobsen et al., J. Phys. Chem. Ref. Data 15, 735 (1986)]. For higher temperatures, the deviation is slightly larger, about 2.5% which still is a very good agreement. The slightly larger difference may be attributed to the vibrational motion not accounted explicitly by rigid rotor approximation, which may be especially important at high temperatures. These results allow to obtain reliable equation of state of nitrogen for pressures up to 30 GPa (300 kbars), i.e., close to molecular nitrogen stability limit, determined by Nellis et al. [Phys. Rev. Lett. 53, 1661 (1984)].