3.3.2 Librational Modes in Solid Nitrogen

The most important differences between the $\alpha$ and $\beta$phases involve the librational motions of the N₂ molecules. Motional narrowing of the nuclear quadrupole coupling by three orders of magnitude and disorder detected in the x-ray structure indicated that molecules in the higher temperature $\beta$ phase do not have their orientations fixed with respect to the lattice; they are disordered by precession-like motion about the ${\hat c}$ axis, with the molecular axes making an average angle of 54.7$^{\circ}$ to the ${\hat c}$-axis. [22]

Raman scattering studies have been able to measure the absorption lines corresponding to the high frequency (2200-2500 cm^-1) molecular stretch mode and the lower frequency (<150 cm^-1) librational and lattice modes at temperatures from 3.6 K to above the $\alpha-\beta$ transition, under equilibrium vapour pressure. [24] As temperature is increased within the $\alpha$ phase, the mean amplitude of librations away from the preferred orientations grows. This is apparent as a slight broadening of the molecular stretch line with increasing T, which is expected when the molecules are no longer in identical environments, beginning at about T=25 K and continuing into the $\beta$ phase.

The low frequency lines, which are sharp at low temperatures in the $\alpha$ phase, gradually become less distinct as the temperature rises to T$_{\alpha\beta}$, and become very broad features above T$_{\alpha\beta}$.This was interpreted as consistent with the build-up of large amplitude, anharmonic librations in the $\alpha$ phase and a fully disordered, precessional motion in the $\beta$ phase.

The disorder introduced by librations is of a short-ranged nature, but since these are soft modes, they are excited at relatively low temperatures - they fall among the acoustic phonons in the excitation spectrum of the lattice.