Nuclear quadrupole spin-lattice relaxation in anharmonic molecular crystals

Abstract

An approach for nuclear quadrupole spin relaxation by anharmonic lattice vibrations of quadrupole nuclei situated at molecular or ion groups is presented. The temperature dependence at constant crystalline configuration is analyzed. This approach takes advantage of the existence of tightly bound molecules or molecular groups. Fluctuations causing relaxation are considered as collective vibrations of the whole lattice. Anharmonicity is explicitly included by involving cubic and quartic terms of the lattice vibrations Hamiltonian. The spectral densities of the spin-lattice Hamiltonian are expressed in terms of the phonon spectral densities and the temperature Green-function perturbation formalism is used for calculating the lower-order contributions. Three kinds of processes are found to contribute mainly to the spin-lattice relaxation time (T, ), namely, anharmonic Raman (AR), first-order Raman (1R), and a third mechanism originated in the self-energy effects on the two-particle spectral density. The AR and e J )2~2( Fcr( t )Fere ) e (2 dt J J

35Cl NQR studies of 1‐chloro‐2,4‐dinitrobenzene and 1,2‐dichloro‐3‐nitrobenzene as a function of pressure and temperature

“…According to the model proposed by Zamar and Gonzalez, 3 the relaxation is assumed to be driven mainly by the fluctuations in the electric field gradient due to the motions of the molecular or ionic group bearing the resonant nucleus. The collective character of the molecular motions is taken into account through the formulation of the lattice dynamics of molecular crystals.…”

35Cl NQR Studies of Bismuth Trichloride

“…The high temperature relaxation is attributed to activated behaviour arising from rotational motions and tumbling or diffusive motions. We find that the Z-G theory [7], which takes into account the collective nature of excitations in a molecular crystal, describes the relaxation behaviour quite well for a wide range of temperature. …”

“…However, deviations from this are reported by many workers [4][5][6]. Recent advances in describing the nuclear quadrupole relaxation in molecular crystals [7] predict that the anharmonic nature of the lattice vibrations plays a significant role in the temperature dependence of Ti in molecular crystals, which may deviate from being proportional to T 2 .…”

“…The deviation of the relaxation rate from the T 2 dependence is an indication that the interaction process described by Z-G is playing an important role in the spin-lattice relaxation. Therefore, we have fitted our T x values to the expression [7] T~l = AT 2 + BT 3 ,…”

“…Since these values are smaller than the usually obtained activation energies [3], it is highly unlikely that the quadrupole relaxation is assisted by any activated process. As BiCl 3 is a molecular crystal, we tried to analyse the quadrupole relaxation with the theory of Zamar and Gonzalez (Z-G) [7], where the collective nature of the molecular motions and anharmonic effects are taken into account. The deviation of the relaxation rate from the T 2 dependence is an indication that the interaction process described by Z-G is playing an important role in the spin-lattice relaxation.…”