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The intergrowth crystal of n -tetracosane/urea presents a misfit parameter, defined by the ratio γ = c h  / c g  ( c  host / c  guest ), that is very close to a commensurate value ( γ ≅ 1/3). High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of γ = 0.3369, which is found to be constant at all temperatures studied. A complex sequence of structural phases is reported. The high temperature phase (phase I) exists in the four-dimensional superspace group P 6 1 22(00 γ ). At T c   1 = 179(1) K, a ferroelastic phase transition increases the dimension of the crystallographic superspace. This orthorhombic phase (phase II) is characterized by the five-dimensional (5D) superspace group C 222 1 (00 γ )(10 δ ) with a modulation vector  a o    * +  c m    * =  a o    * + δ ·  c h    * , in which the supplementary misfit parameter is δ = 0.025(1) in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about 440 ± 16 Å). At T c   2 = 163.0(5) K, a 5D to 5D phase transition leads to the crystallographic superspace group P 2 1 2 1 2 1 (00 γ )(00 δ ) with a very similar value of δ . This phase transition reveals a significant hysteresis effect.

Long-range modulation of a composite crystal in a five-dimensional superspace