A qualitative account is given of the main processes whereby a paramagnetic spin system attains thermodynamic equilibrium with the lattice in which it is embedded. The basic theory needed for calculating the spin-lattice relaxation times governing the rate of establishment of equilibrium between the two systems is sketched. It is possible to produce microwave phonons of the right frequencies for use in ultrasonic spin-resonance experiments, to observe directly the interaction between the spin system and phonons of a particular frequency and so avoid complications inherent in the conventional spin-lattice relaxation experiments (where a thermal distribution of phonons is involved).