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 = ch /cg (chost/cguest), 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 Tc1 = 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 ao* + cm* = ao* + δ · ch*, 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 Tc2 = 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.

The creation of modulated monoclinic aperiodic composites in n-alkane/urea compounds.

n-Dodecane/urea is a member of the prototype series of n-alkane/urea inclusion compounds. At room temperature, it presents a quasi-one dimensional liquid-like state for the confined guest molecules within the rigid, hexagonal framework of the urea host. At lower temperatures, we report the existence of two other phases. Below Tc=248 K there appears a phase with rank four superspace group P6122(00γ), the one typically observed at room temperature in n-alkane/urea compounds with longer guest molecules. A misfit parameter, defined by the ratio γ=ch /cg (chost/cguest), is found to be 0.632±0.005. Below Tc1=123 K, a monoclinic modulated phase is created with a constant shift along c of the guest molecules in adjacent channels. The maximal monoclinic space group for this structure is P1211(α0γ). Analogies and differences with n-heptane/urea, which also presents a monoclinic, modulated low-temperature phase, are discussed.

A molecular "phase ordering" phase transition leading to a modulated aperiodic composite in n-heptane/urea.

n-Heptane/urea is an aperiodic inclusion compound in which the ratio of host and guest repeats along the channel axis is very close to unity and is found to have a constant value (0.981) from 280 K to 90 K. Below 280 K, two phase transitions are observed. The first (T(c1) = 145 K) is a ferroelastic phase transition that generates superstructure reflections for the host while leaving the guest with 1D order. The second (T(c2) = 130 K) is a "phase ordering" transition to a four-dimensional structure (P2(1)11(0ßγ)) with pronounced host-guest intermodulation and a temperature dependent phase shift between guests in adjacent channels.

Confined linear molecules inside an aperiodic supramolecular crystal: the sequence of superspace phases in n-hexadecane/urea.

High-resolution studies of the host-guest inclusion compound n-hexadecane/urea are reported at atmospheric pressure, using both cold neutrons and x-ray diffraction. This intergrowth crystal presents a misfit parameter, defined by the ratio c(h)/c(g) (c(host)/c(guest)), which is temperature independent and irrational (γ = 0.486 ± 0.002) from 300 to 30 K. Three different structural phases are reported for this aperiodic crystal over this temperature range. The crystallographic superspaces are of rank 4 in phases I and II, whereas phase III is associated with an increase in rank to 5, with a supplementary misfit parameter (δ = 0.058 ± 0.002) that is constant throughout this phase. The superspace group of phase I is hexagonal P6(1)22(00γ) down to T(c1) = 149.5 ± 0.5 K; phase II, which persists down to T(c2) = 127.8 ± 0.5 K is orthorhombic P2(1)2(1)2(1)(00γ), and phase III is orthorhombic P2(1)2(1)2(1)(00γ)(00δ).

Hidden degrees of freedom in aperiodic materials.

Numerous crystalline materials, including those of bioorganic origin, comprise incommensurate sublattices whose mutual arrangement is described in a superspace framework exceeding three dimensions. We report direct observation by neutron diffraction of superspace symmetry breaking in a solid-solid phase transition of an incommensurate host-guest system: the channel inclusion compound of nonadecane/urea. Strikingly, this phase transition generates a unit cell doubling that concerns only the modulation of one substructure by the other-an internal variable available only in superspace. This unanticipated pathway for degrees of freedom to rearrange leads to a second phase transition, which again is controlled by the higher dimensionality of superspace. These results reveal nature's capacity to explore the increased number of phases allowed in aperiodic crystals.

Unanticipated guest motion during a phase transition in a ferroelastic inclusion compound.

Urea inclusion compounds (UICs) have been used as tools to understand ferroelastic domain switching and molecular recognition during crystal growth. Although the vast majority of UICs contain helical arrangements of host H-bonds, those containing guests with the formula X(CH(2))(6)Y (X, Y = Br, Cl, CN, NC) adopt an alternative P2(1)/n packing mode in which the host molecules exist as stacked loops of urea hexamers. Such structures may be further separated into two classes, ones distorted away from hexagonal symmetry along [100] (Br(CH(2))(6)Br, Br(CH(2))(6)Cl, and Cl(CH(2))(6)Cl) and those distorted along [001] (e.g. NC(CH(2))(6)CN). In each of these systems, guests exist as equilibrium mixtures of gauche conformers whose populations control the direction and magnitude of the observed distortion. Such UICs are potentially ferroelastic, but the n-glide requires that domains are not related by a simple rotation-translation mechanism as in the helical systems. Ferroelastic (degenerate) domain reorientation would necessitate a large-scale reorganization of the urea framework and rupture of numerous H-bonds. Coupled with distortions of 2 to 10%, this mechanism-based barrier to domain switching has precluded observation of this phenomenon. To prepare ferroelastic UICs with minimal distortions from hexagonal symmetry, attempts were made to form solid solutions of UICs containing guests from the two classes. This failed, however: solid solution formation of the stacked loop form is usually possible within a series (e.g. with Cl(CH(2))(6)Cl and Br(CH(2))(6)Br), but not between series (e.g. Cl(CH(2))(6)Cl and NC(CH(2))(6)CN). Crystals of Cl(CH(2))(6)CN/urea, in which a single guest contains substituents from each class, are distorted along [001] by only 0.5% from hexagonal symmetry at 298 K and exhibit ferroelastic domain reorientation at high forces. At -66 degrees C, Cl(CH(2))(6)CN/urea undergoes a topotactic phase transition that is unexpectedly nontopochemical. The structure of the low-temperature phase, including the orientation of the methylene chain, closely matches the structures of UICs distorted by 10% along [100] (e.g. Cl(CH(2))(6)Cl/urea). In this transition, small conformation changes of guests give rise to large-scale guest translations of approximately 5.5 A down the channel axis, even though an analogous gauche-to-gauche jump is well established in closely related materials that adopt either high- or low-temperature forms (e.g. NC(CH(2))(6)CN/urea, Cl(CH(2))(6)Cl/urea). The large guest displacement during this transition explains the difficulty in preparing solid solutions of the P2(1)/n form with guests of formula X(CH(2))(6)Y from two different series (e.g. Cl(CH(2))(6)Cl and NC(CH(2))(6)CN). This failure arises not from the different orientations of guest-induced strain, but from preferential occupation of different sites along the channel by the two types of guests. The subtlety of this process and of the interactions involved highlights the difficulty in using simple considerations of isomorphism to design new materials.

Crystal engineering: from structure to function.

Modern crystal engineering has emerged as a rich discipline whose success requires an iterative process of synthesis, crystallography, crystal structure analysis, and computational methods. By focusing on the molecular recognition events during nucleation and growth, chemists have uncovered new ways of controlling the internal structure and symmetry of crystals and of producing materials with useful chemical and physical properties.