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



Citation: Guerin, L., Mariette, C., Rabiller, P., Huard, M., Ravy, S., Fertey, P., . . . Toudic, B. (2015). Long-range modulation of a composite crystal in a five-dimensional superspace. Physical Review B, 91(18), 7. doi:10.1103/PhysRevB.91.184101
The intergrowth crystal of n-tetracosane/urea presents a misfit parameter, defined by the ratio gamma = c(h)/c(g) (c(host)/c(guest)), that is very close to a commensurate value (gamma congruent to 1/3). High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of gamma = 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 P6(1)22(00 gamma). At T-c1 = 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 C222(1)(00 gamma)(10 delta) with a modulation vector a(o)* + c(m)* = a(o)* + delta . c(h)*, in which the supplementary misfit parameter is delta = 0.025(1) in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about 440 +/- 16 angstrom). At T-c2 = 163.0(5) K, a 5D to 5D phase transition leads to the crystallographic superspace group P2(1)2(1)2(1)(00 gamma)(00 delta) with a very similar value of delta. This phase transition reveals a significant hysteresis effect.


Urea Inclusion-Compounds, X-Ray-Diffraction, Phase-Transition, N-Paraffins, Compounds Oc(Nh2)2+Cnh2N+2, Aperiodic Crystals