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

The intergrowth crystal of n-tetracosane/urea presents a misfit parameter, defined by the ratio γ = c /c (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 P6₁22(00γ). At T₁ = 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 C222₁(00γ)(10δ) with a modulation vector ^* + ^* = ^* + δ · ^*, 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 T₂ = 163.0(5) K, a 5D to 5D phase transition leads to the crystallographic superspace group P2₁2₁2₁(00γ)(00δ) with a very similar value of δ. This phase transition reveals a significant hysteresis effect.