Neutron diffraction studies of domain growth associated with the 50 K anomaly in Pd-D

At around 50 K, the PdDx system (0.63 < x < 0.69) undergoes a second-order phase transition to a superlattice structure in which the deuterons on the octahedral sites in the f.c.c. lattice of palladium adopt a new structure with space group I4(1)/amd. This structure is characterized by a superlattice reflection at (1, 1/2, 0) which, for a single-crystal sample, can be easily observed using neutron diffraction. The transition is second order and is known to involve complex time dependencies. In the present experiment, the evolution of the superlattice peak with time and temperature was investigated in a single-crystal sample using high resolution neutron diffraction. The peak shape was analysed in terms of three components, the narrowest of which appears below the critical temperature and is best represented by a lorentzian-squared form corresponding to diffraction from ordered domains where the probability of remaining in the same domain decreases exponentially with distance. Annealing causes this peak to narrow while retaining the same shape, which is characteristic of scaling behaviour. The width parameter was found to increase initially as the square root of time but then to flatten out. This behaviour can be explained in terms of the Nernst-Einstein relationship if account is taken of the build-up of elastic strain energy arising from the tetragonal symmetry of the superlattice.