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The spin lattice relaxation of I=3/2 quadrupolar spin system due to domainwalls in order-disorder ferroelectrics has been studied and a general method isproposed for the measurement of domain width in nano ferroelectrics. Based onthe fact that electric polarization undergoes spiral orientation as one movesfrom one domain to the other, it is assumed that at low temperatures the spinsat and near domain walls undergo relaxation due to possible easy reorientationof electric polarization in domain walls even though such a relaxation in themain body of the domain has almost ceased. The spins present inside the domainundergo relaxation through transfer of magnetization to the domain wallsthrough a spin diffusion process by nearest neighbour interaction. Rateequations for spin populations are formed by representing the ferroelectricdomain by a one-dimensional chain of equidistant spins having dipolar coupling.Spin populations are calculated as a function of time for different ratios ofquadrupolar to dipolar transition probabilities for a sample subjected toselective rf pulse. Expression for spin- lattice relaxation time T1 is derivedin terms of domain width and ratio of quadrupolar to dipolar transitionprobabilities. It is found that the domain width can be estimated provided thevalue of spin lattice relaxation time T1 is known for the corresponding crystalwith normal sized grains. The results are quite general and can be applied toany order disorder ferroelectric with nano sized domains and having spin I=3/2nuclei.

Estimation of Domain Size in Nano Ferroelectrics from NMR T1 Measurements