Spin-lattice relaxation in the dipolar and rotating frames due to correlated ultraslow motions: Order-disorder-type crystals

In the ultraslow-motion case an expression for the dipolar spin-lattice relaxation time is derived, which is convenient for both correlated and uncorrelated motions. $T_{1D}$ is related to the first derivative of the dipolar Hamiltonian autocorrelation function. The Slichter-Ailion expression for $T_{1D}$ is obtained as a special case. Results are applied to the order-disorder-type crystals which can be described by an Ising model, where the necessary correlation functions have simple forms in the random-phase approximation. The relaxation in the rotating frame is briefly discussed. A summary is given of critical effects on the nuclear-spin-lattice relaxation for both ultraslow motion and faster motion.