Landau theory of incommensurate phases in thiourea

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Abstract
The phenomenological Landau-type free-energy expansion which contains only second-, third- and fourth-order invariants of the order parameter is proposed for thiourea. The finite set of harmonics and subharmonics which completely describe any commensurate phase is specified. The observed phases 1/3, 1/7, 1/8 and 1/9 arise owing to the couplings of the Umklapp type between higher harmonics. The reasons for the disappearance of the phase 1/7 at high pressure are discussed. The commensurate phases n/m where n and m are any integers, also follow from the free-energy expansion. The results of numerical calculations show the existence of harmonics and subharmonics for high commensurate phases. The subharmonics are related to discommensurations.