Schematic structure of an n-alkane/urea. (a) n-Heptane/urea containing arbitrarily positioned guests along the channel axis. (Here, ch = 11.0 Å, cg = ch/γ with γ = 0.981). (b) (a,b) Plane projection of a hexagonal UIC showing the basic vectors a hex and b hex of the hexagonal phase and basic vectors a and b of the low symmetry phases. (c) Two-dimensional representation of a UIC indicating the definitions of c h , c g , and Δ g , the offset between guest molecules in adjacent channels.
Section of a channel axis oscillation x-ray image of n-heptane/urea in phases I (T = 200 K), II (T = 140 K), and III (T = 90 K). The detector distance is 300 mm. In phases I (host: hexagonal P6122) and II (host: monoclinic P2111), the guest diffraction image appears as diffuse bands perpendicular to c g * . In phase II, white arrows indicate host superstructure Bragg peaks with indices h = 1, k = 2, l = 0, 1, and 2 in the low symmetry notation. In phase III, black arrows indicate guest Bragg peaks ((1, 1, 0, 1) and (1, 1, 0, 2) appearing on the diffuse bands. Bottom: enlargement of the reciprocal zone around the (1, 2, 2, 0) and (1, 1, 0, 2) Bragg peaks showing the host periodicity (at 2) and guest periodicity (at 2γ = 1.962) along the aperiodic c* direction.
(a) and (b) Diffraction images in the high symmetry phase (phase I) at T = 200 K. (a) (b*, c*) diffraction image obtained with Mo Kα radiation and a sample to detector distance of 50 mm. The red circles indicate the (0, 0, 6) and (0, 0, 12) Bragg peaks. (b) (a*, c*) diffraction image obtained with Cu Kα radiation and a sample to detector distance of 150 mm. (c) (a*,b*) and (d) (a*,c*) diffraction images of phase II at T = 133 K obtained with Cu Kα radiation and a sample to detector distance of 150 mm. In Figure (c), dashed and plain red circles indicate the (0, 3, 0) Bragg peaks from two different domains (2π/6 rotation about c h *).
Temperature evolution of a host superstructure Bragg peak (1, 2, 2) appearing in phase II, defining the transition temperature of Tc1 = 145 K.
Reconstructed (0, k, l, m) (a) and (1, k, l, m) (b) images for phase III of n-heptane/urea at 90 K (detector distance = 150 mm). As shown by the red lines, which refer to the mean reciprocal lattice of the alkane guest, the guest subsystem is monoclinic. Solid and dashed red lines refer to two different domains with c g± * = ±βb * + γc h * . In a given domain, systematic extinctions for (h+k) odd indicate a C-centered monoclinic lattice for the guest. Supplementary Bragg peaks appear by virtue of the intermodulation (satellite reflections (h, k, l, m) with l and m being different from 0; see green arrows). Satellites with higher order components (up to l = 5 and m = 3) have been observed with laboratory equipment (not shown). (c) Reconstruction of the (h, k, 0, 1) and (h, k, 0, 2) layers at 90 K. Hexagons are guides for the eyes and refer to six equivalent domains (2π/6 rotation about c*). The 3D reciprocal pattern of these six domains is schematized in (d).
(a) Temperature evolution of the misfit parameter β = 2Δg/cg (black squares). (b) Temperature evolution of the intensity of the guest Bragg peaks l = 0 and m = 1 (solid red circles), l = 0 and m = 2 (open red circles), and satellite Bragg peaks l = 1 and m = 1 (blue triangles), all normalized at 114 K. (c) Schematic representation of n-heptane/urea in phase III with mean host and guest monoclinic cells. In the limit of precision of our measurements, the angle αh is found to be 90°. The difference between the lengths of ch and cg has been exaggerated. Furthermore, a different origin along the channel direction is given for host and guest subsystems to stress the fact that they are aperiodic in this direction. (d) Projection of the unit cells along the channel axis. In the projection, the urea substructure is represented as black hexagons, and the normal basis vectors a and b are drawn as black arrows. The red numbers indicate the relative mean positions of alkane molecules along the channel axis, in Δg units.
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