Modulated phases, memory effect and defect density waves in thiourea

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Abstract
In this paper, we review a variety of recent experimental and theoretical results on thiourea, a compound known for the richness of its phase diagram. We show that a continuum approach “à la Landau” is particularly well suited to understand the modulated phases and the commensurate lock-ins in this compound. The locked phase of commensurability order 8 is qualitatively and semi-quantitatively well accounted for. The birefringence anomalies which detect this phase are shown to be related to the gradient amplitude coupling term in the free energy. Our analysis allows an order of magnitude estimate for the thermal extension of high commensurability order lock-ins. We conclude that wide steps of commensurability order 29, or 43 cannot be of intrinsic origin, and that their observation by X-ray spectroscopy is due to irradiation defects. We describe, discuss and analyse theoretically the memory effect of nodulated phases, which we ascribe to the condensation of a Defect Density Wave, due to the diffusion of mobile impurities in the modulation periodic potential. The kinetics of this condensation are discussed within a simple model, which assumes the modulation to be rigid. Applications of the memory effect are discussed and illustrated. Although most results are derived in the single harmonic approximation for the order parameter, we discuss briefly the effect of higher order harmonics. The general conclusion of the paper points to the rôle of impurities, especially mobile ones, in modulated structures.