(a) Coordinate definition for linear-molecule orientation. is the molecular orientation vector, which rotates an angle θ off its nominal orientation . , , and are mutually orthogonal. represents the projection of vector on the plane that is perpendicular to . (b) Graphical illustration of the relationship between the rotation angle and the spherical surface area. is the nominal molecular orientation. The shaded blue spherical cap represents the surface area, 2π(1 − cosθ), around within the angle θ.
Illustration of the alternating layers of unit cell A and B for the artificial “low-temperature” β-N2 phase structure.
Molecular geometry of Etters et al.'s nitrogen model. Size of nitrogen atom centers is not drawn to scale.
χ i vs. temperature for α-N2. Legend indicates the molecular density in Å−3.
Plots of ⟨cos θ⟩ probability distribution for molecular densities, ρ [Å−3], of (a) 0.0230, (b) 0.0225, (c) 0.0220, (d) 0.0215, and (e) 0.0210. Legend indicates the temperature in Kelvin.
Plot of βA/N vs. 1/N for α-N2 phase at ρ = 0.0230 Å−3 and T = 30 K, where N is the number of particles and βA/N is from Eq. (2).
TPTrans path. χ i vs. temperature in Kelvin. Legend indicates molecular density in Å−3.
Free energy difference for initial, orientation-coupling perturbation of RP perturbation path, as function of molecular density, ρ.
RP path. χ i vs. constraint angle, θmax , in degrees. Legend indicates molecular density in Å−3.
TP path.χ i vs. temperature in Kelvin. Legend indicates molecular density in Å−3.
βA C /N vs. 1/N plot for different perturbation paths at ρ = 0.0230 Å−3 with 432-, 1024-, and 2000-particle system sizes. The perturbation paths presented in the plot are (a) TPTrans, (b) RP, and (c) TP.
Plot of βA/N vs. 1/N for β-N2 phase at ρ = 0.0230 Å−3 and T = 45 K, where βA/N is from Eq. (16). The harmonic contribution represents that formulated at the outset of the TPtrans path, and thus is defined with respect to the system with rigid molecular orientations.
Plot of Gibbs free energy vs. temperature. Legend indicates the pressure for each set of curves.
P-T diagram of solid-phase nitrogen. α-N2 is stable at lower temperatures and β-N2 is at higher temperatures. The uncertainty reported for the data from this work is about the size of the symbols.
Examination of contributing terms in Helmholtz free-energy calculation per particle [in unit Kelvin] for α-N2 and β-N2 phase at ρ = 0.0230 Å−3, and T = 49 K. The last digit in the parentheses is the 67% confidence limit.
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