Solid Nitrogen: A Nuclear Quadrupole Resonance Study (1971)

Nuclear quadrupole resonance of $^{14}\mathrm{N}(I=1)$ has been studied for the two diatomic species $^{14}\mathrm{N}$-$^{14}\mathrm{N}$ and $^{14}\mathrm{N}$-$^{15}\mathrm{N}$ in solid $\ensuremath{\alpha}$-nitrogen. Spectra from carefully prepared and annealed samples display well-resolved intramolecular dipolar splittings consisting of an asymmetric triplet for $^{14}\mathrm{N}$-$^{14}\mathrm{N}$ and a doublet for $^{14}\mathrm{N}$-$^{15}\mathrm{N}$. From the order of the components of the triplet, the sign of the nuclear quadrupole coupling constant is deduced to be negative. Measurements of the resonance frequencies ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$ and ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}15)$ have been made as a function of temperature from 4.2 K to the phase transformation at 35.6 K, and as a function of isotopic concentration for five concentrations ranging from 0.37 to 99% $^{15}\mathrm{N}$. The hydrostatic pressure dependence of ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$ in a natural isotopic abundance sample has been observed at seven fixed temperatures. These results were combined with detailed thermal expansion and compressibility data to obtain the resonance frequency ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$ as a function of temperature at constant volume and as a function of volume at constant temperature. The observed strong temperature dependence of the resonance frequency is ascribed to excitation of large-amplitude molecular librations having substantial anharmonic character. A quasiharmonic theory of motional averaging incorporating published Raman spectroscopy data provides a satisfactory fit to the resonance frequency at zero pressure. An independent determination of the motional averaging obtained from the dipolar splitting is in excellent agreement with the averaging of the quadrupole resonance frequency. A fit of the theoretical equation for motional averaging with the experimental volume dependence of ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$ yields the volume dependence of the libration frequencies. Three isotopic mass effects were observed and studied at 4.2 K: (i) The frequencies ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$ and ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}15)$ increase approximately linearly with increasing concentration of $^{15}\mathrm{N}$ (isotope shift); (ii) ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}15)\ensuremath{-}{\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)=7.95\ifmmode\pm\else\textpm\fi{}0$. 30 kHz independent of concentration (isotope splitting); and (iii) the individual lines of the spectra broaden in mixed samples due to dynamic disorder. The total isotope shift is 2.6 \ifmmode\pm\else\textpm\fi{} 0.25 kHz for both molecules; a qualitative explanation of the effect is given based on the volume dependence of ${\ensuremath{\nu}}_{Q}(14\ensuremath{-}14)$, the known difference in lattice constants of pure $^{14}\mathrm{N}_{2}$ and $^{15}\mathrm{N}_{2}$,and the assumption of a defect volume for a $^{14}\mathrm{N}$-$^{14}\mathrm{N}$ impurity molecule in a $^{15}\mathrm{N}_{2}$ lattice. The isotope splitting is a consequence of unequal masses and force constants for the two molecules.