Memory and Perfection in Ferroelastic Inclusion Compounds - Crystal

Memory and Perfection in Ferroelastic Inclusion Compounds† Hollingsworth,*,‡

Peterson,‡,§

Rush,‡

Mark D. Matthew L. Jeremy R. Michael E. Brown,| Mark J. Abel,‡ Alexis A. Black,‡ Michael Dudley,⊥ Balaji Raghothamachar,⊥ Ulrike Werner-Zwanziger,|,¶ Ezra J. Still,| and John A. Vanecko|

CRYSTAL GROWTH & DESIGN 2005 VOL. 5, NO. 6 2100-2116

Department of Chemistry, Kansas State University, Manhattan, Kansas 66506, Department of Materials Science and Engineering, State University of New York at Stony Brook, Stony Brook, New York 11794, and Department of Chemistry, Indiana University, Bloomington, Indiana 47405 Received July 19, 2005

W This paper contains enhanced objects available on the Internet at http://pubs.acs.org/crystal. ABSTRACT: In a series of ferroelastic urea inclusion compounds (UICs), in which domain reorientation occurs upon application of an external anisotropic force, introduction of a relaxive impurity that disrupts a specific hydrogenbonding network transforms a plastic (irreversible) domain-switching process into one that exhibits a striking memory effect and “rubber-like behavior”, a form of pseudoelasticity. As expected for a highly cooperative process, the ferroelastic response to the impurity concentration exhibits a critical threshold. Through synchrotron white-beam X-ray topography (SWBXT) of crystals under stress, videomicroscopy of spontaneous repair during crystal growth, acoustomechanical relaxation of daughter domains, kinetic measurements of spontaneous domain reversion, and solid-state 2H NMR of labeled guests, this work shows how relaxive impurities lower the barrier to domain switching and how differences in perfection between mother and daughter domains provide the driving force for the memory effects. Although the interfacial effects implicated here are different from the volume effects that operate in certain shape memory materials, the twinning and defect phenomena responsible for the rubber-like behavior and memory effects should be generally applicable to domain switching in ferroelastic and ferroelectric crystals and to other solid-state processes. Introduction Elasticity is an important cooperative phenomenon1 whose understanding is crucial to fields as diverse as materials science, where resilience and flexibility are important,2-4 and geophysics, where fracture, creep, and phase transitions are studied extensively.5,6 As shown by McBride and co-workers, it plays a key role in the photoreactivity of solids,7-11 where anisotropic relaxation of local and long-range stress is of paramount importance. It should also be critically important in the domain switching of technological devices such as ferroelectric liquid crystals12 and in epitaxial growth on surfaces.13 A detailed understanding of elasticity of materials requires not only a local picture of intermolecular interactions14 and their anharmonicities15 but also a longer range view of the cooperative mechanisms that control behavior in the bulk. For many important materials such as polymers and liquid crystals, neither is readily available, because structural disorder often blurs the mechanistic view of plastic deformation or * To whom correspondence should be addressed. Tel: 785-532-2727. Fax: 785-532-6666. E-mail: [email protected]. † Dedicated to Prof. J. Michael McBride on the occasion of his 65th birthday. § Current address: TransForm Pharmaceuticals, Inc., 29 Hartwell Ave., Lexington, MA 02421. ‡ Kansas State University. | Indiana University. ⊥ State University of New York at Stony Brook. ¶ Current address: Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3.

elastic return to the parent structure. Single crystals of simple molecular materials that undergo observable elastic phenomena provide an important avenue for probing the elastic properties of solids. Ordinarily, each system must be considered on a case-by-case basis, since crystal packing is rarely the same, even for compounds of similar structure. To allow comparison among different systems, it is desirable to find materials that can be tailored or perturbed in predictable ways. Molecular inclusion compounds provide unique opportunities to unravel the molecular determinants of domain switching. Just as in McBride’s seminal work on photoreactivity of long-chain diacyl peroxides, the use of inclusion compounds allows one to generate either homologous series or closely related materials in which either isomorphous or nonisomorphous crystal packing can be achieved and compared.9,10,16,17 In this paper, we focus on channel inclusion compounds of urea containing 2,10-undecanedione (1) and on mixed crystals containing 1 and 2-undecanone (2). These crystals are ferro-

elastic;18-24 that is, they exhibit different domain orientations that can be interconverted through the application of an external anisotropic force.25 Such ferroelastic

10.1021/cg050347j CCC: $30.25 © 2005 American Chemical Society Published on Web 10/12/2005

Ferroelastic Inclusion Compounds

crystals are closely related to ferroelectric and ferromagnetic materials, in which the orientation states are defined by either spontaneous electric or magnetic polarizations, and for which the switching between states is accomplished with external electric or magnetic fields. Our continued interest in the ferroelastic properties of crystals arises because many ferroelectric crystals are also ferroelastic, and the two properties are strongly coupled.26 A clearer understanding of domain switching in such ferroelastoelectrics requires that we identify the roles that elasticity and cooperativity play in controlling the barriers to domain switching in ferroelastic materials. In mixed crystals of 1 + 2 in urea, 2 acts as a relaxive impurity that disrupts a specific hydrogen-bonding network and transforms a plastic (irreversible) domain switching process into one that exhibits a striking memory effect and “rubber-like behavior”, in which reversion of the daughter back to the parent orientation involves spontaneously reversible motions of twin boundaries. Such rubber-like behavior is a form of “pseudoelasticity”, which encompasses any process (including stress-induced transformations, which are termed superelastic) in which an apparently plastic deformation is characterized by a closed-loop stress-strain curve and recovers by release of stress at a constant temperature.27-29 As expected for a highly cooperative process, the ferroelastic response to the impurity concentration exhibits a critical threshold effect. Through synchrotron whitebeam X-ray topography (SWBXT) of crystals under stress, videomicroscopy of spontaneous repair during crystal growth, acoustomechanical relaxation of daughter domains, kinetic measurements of spontaneous domain reversion, and 2H NMR of selectively deuterated guests, we show here how relaxive impurities lower the barrier to domain switching and how differences in perfection between mother and daughter domains provide the driving force for the memory effects. In particular, SWBXT reveals the presence of invisible, nanoscopic twins that are thought to be epitaxially matched with the surrounding mother domain, but mismatched with the daughter generated by application of anisotropic stress. Although they are different from the ones that appear to predominate in certain shape memory materials, the twinning and defect phenomena responsible for the rubber-like behavior and memory effects may be generally applicable to domain switching in ferroelastic and ferroelectric crystals and to other solidstate processes. Experimental Section Crystal Growth. Crystals of (1 + 2)/urea were typically grown by suspending sealed flasks containing methanol solutions of 1, 2, and urea (2.5 M urea, 9:1 host:guest ratio) in a water-filled Dewar flask at 40 °C and cooling to room temperature. Typically, crystals first appeared between 29.5 and 27.5 °C; in this temperature range the cooling rate was approximately 1.8 °C h-1. Crystallization was allowed to continue overnight, after which the crystals were collected by spreading onto lens paper. They were stored in argon-flushed vials at 3 or -20 °C. The crystal used in the acoustomechanical experiment (Figure 7 below) was grown by cooling a mixture of 1 and 2 (84.2:15.8 mole ratio) and urea that had been dissolved in a 65:35 (v:v) mixture of MeOH and EtOH. In comparison to MeOH, this mixed solvent system led to lower incorporations of 2 and occasional growth banding (as evi-

Crystal Growth & Design, Vol. 5, No. 6, 2005 2101 denced by changes in retardation in birefringence maps). Birefringence maps for crystals grown from MeOH generally yielded quite uniform retardations within a given growth sector,23 suggesting that growth banding is not a serious problem, even though the crystals were grown under quiescent conditions. In this solvent, however, incorporation of 2 is preferred over 1 by a factor of 1.3; thus, small gradients in composition may be expected as crystallization proceeds. Such gradients are minimized by crystallizing under these lowyielding conditions (25-40%). Stress-Strain Experiments. The ultrafast stress-strain device used for kinetic studies was designed and built locally by the authors and by members of the Electronics Design Laboratory and the Advanced Manufacturing Institute of Kansas State University. The details of this device will be described in a forthcoming publication. In essence, it consists of a series of stacked piezoelectric transducers that can accurately control the position of a zirconia bar (the stress anvil) in 20 nm increments while measuring the applied force. Other stress-strain experiments, as well as those performed at Brookhaven National Laboratory, involved devices utilizing manual strain adjustment (with a screw) and either analog or digital stress gauges. The device used in the experiment with the piezoelectric transducer followed (in part) the design of Burkhardt et al.30 A typical strain experiment was carried out on a Nikon Microphot-SA microscope equipped with crossed polarizers and a 530 nm λ plate. Experiments were documented by a combination of still photographs from a Nikon D1 digital camera and video recorded using a Sony Hyper HAD CCD camera. The flat (001) plates were typically 1-2 mm wide by at least 100 µm thick (along [001]). The point of initial strain was denoted as the position where the stress reading became nonzero and no visible movement of the crystal could be detected. From photographs, the effective width of the crystal at zero strain, L0, was measured in Adobe Photoshop (v. 5.5 for the Macintosh). The percent strain, S, is defined as the amount of compression of the crystal as a percentage of the width of an unstressed crystal (100(L0 - L)/L0). In determination of the plastic-elastic threshold, crystals were held in the extinguishing position and compressed at room temperature to an appropriate strain in 1 µm increments. Release was performed in a similar fashion. Crystals whose daughters retreated fully (i.e. to the extinguished orientation) were deemed “elastic” (at the strain achieved) and were typically strained again to a higher value of S. Crystals whose daughters did not fully retreat were deemed “plastic”. Following the stress-strain experiments, the compositions of individual sectors were determined with HPLC. Because the stress-strain device can retract the stress bar at an initial rate of 27 cm s-1, kinetic measurements of ferroelastic domain reversion were possible. In these experiments pristine (uncut) crystals were compressed (usually to 0.4-1.2% strain), and the stress bar was retracted by 300 µm at the fastest possible rate. To minimize inevitable crystal translation immediately following retraction of the stress bar, a thin film of Paratone oil was applied to the bottom side of the crystal. Events were recorded with a Kodak MotionCorder SR-Ultra high-speed video camera coupled to the stress-strain device through a Kodak Multichannel Data Link or with an X-StreamVision XS-4 high-speed camera (on loan from Speed Vision Technologies, Inc.). Although the camera resolutions are different, both systems are capable of recording 10 000 frames per second (fps). Illumination in the fast video experiments was provided by an EXFO X-Cite XE-120 light source. Ultrafast video was converted to individual frames with Adobe Premiere 5 or X-Stream X-Vision 1.05 (both for Windows). High-speed video frames were analyzed with Adobe Photoshop 5.5 for the Macintosh. In a stress experiment in which the original mother domain was held in the extinguishing position, the daughter appeared as a bright region in the film. The average luminosity of the region of the frame of intereststhe sample areaswas measured using Photoshop. If the crystal moved, this sample area was repositioned manually according to notable landmarks on the crystal to ensure that

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the same region was measured throughout the relaxation event. Using the known unit cell dimensions, the thickness of the crystal, and the rate of change in luminosity (which was taken to be proportional to the rate of channel reversion) the rates of domain reversion (moles of guest s-1) were calculated. Acoustomechanical relaxation was performed by placing a 12 V Piezo Mini Buzzer (Radio Shack Part No. 273-074, 4.1 kHz resonant frequency) on the microscope stage approximately 1.5 cm from the crystal so that the primary direction of sound output was along the channel axis of the crystal [001]. The sound pressure output for this device is rated at 70 dB (minimum) at 30 cm and 12 V. During the experiments shown in Figure 7, the buzzer was operated at 15 V. X-ray Topography. Synchrotron white beam X-ray topography (SWBXT) images31 were collected at the Stony Brook Synchrotron Topography facility, beamline X-19C, at the National Synchrotron Light Source, Brookhaven National Laboratory. All diffraction images were recorded in transmission mode on Kodak SR-1 high-resolution X-ray film. The detector consisted of a film cassette placed perpendicular to the X-ray beam and approximately 15 cm from the sample. In these experiments, the crystal was epoxied to a nylon mount that was attached to a eucentric goniometer head. A stress device utilizing an analog dynamometer was used to apply uniaxial force along the goniometer axis to the crystal. Videomicroscopy was performed using the same Sony video camera described above with a 0.75-3.0× microscope attachment (Model R55-140) from Edmund Scientific, utilizing rotatable polarizers on either side of the sample and a 530 nm λ plate. This microscope assembly was attached to a rack that allowed it to be moved in and out of alignment with the crystal’s [001] axis without disturbing the crystal or the stress device. The X-ray topographs were indexed using the program Lauept (written by Dr. XianRong Huang of the Department of Materials Science and Engineering, SUNY Stony Brook, Stony Brook, NY) and the reported crystal structure of 2,10undecanedione/urea.18 X-ray Diffraction of Crystals under Stress. A stressstrain device mounted to a eucentric goniometer head was used to measure diffraction patterns of crystals under stress. Intensity measurements were made on a Siemens P4 goniostat and a Bruker SMART 1000 system with graphite-monochromated, sealed-tube Mo KR (λ ) 0.710 73 Å) radiation. The distance from the crystal to the detector was 5 cm for in situ stress experiments and 10 cm for cell constant determination and indexing. Photographs using crossed polars and a λ plate were taken with a Nikon D1 camera attached to the P4 telescope mounting bracket. Guest Analysis. Because the ratio of 1 and 2 in a given sector can vary from the nominal (solution) content, individual sectors that had undergone domain switching were cleaved with a scalpel and analyzed by HPLC for guest composition. Rotational twins extending over more than one growth face were cleaved, and the segments were analyzed separately. Other sectors were analyzed for comparison. Samples were dissolved in Acros HPLC “gradient grade” methanol. The HPLC system consisted of a Waters 2690 autosampler and pump with Waters 486 UV detector (set at 275 nm, the λmax for ketones in the elution solvent) and DuPont Zorbax ODS C18 column (4.6 mm by 25 cm in length; 5 µm beads). A fixed eluent of 24% water, 40% CH3CN, and 36% MeOH was used at a flow rate of 1 mL min-1. The solvents were Acros HPLC “gradient grade,” and the water was deionized and filtered through a Barnsted filtration system. Up to four 50 µL injections of each sample were used; periodically a standard containing a known ratio of 1 and 2 was injected to monitor HPLC performance and to help establish the limits of accuracy for the sample injections. Birefringence Mapping. The Metripol microscope (Oxford Cryosystems) utilizes a rotating polarizer-λ/4 plate-analyzer to map the birefringence for each pixel in an image.32,33 In this device, intensity maps are collected for a series of polarizer orientations, and a Fourier analysis of the intensity variation gives rise to three maps: intensity, indicatrix orientation (φ),

Hollingsworth et al. and phase retardation between the eigenrays as |sin(δ)|. With small retardations, data collected at one wavelength are sufficient to establish the direction of the slow axis. For larger retardations, it is possible to establish the absolute retardation (δ) by collecting intensity data at three wavelengths.33 In the example shown in Figure 5 below, the crystal was thin enough to avoid Fourier artifacts that are inherent in thick crystals that are strongly birefringent. Solid-State NMR. 2H NMR spectra were taken of polycrystalline samples at 7.04 T on a Tecmag NMR system with a Chemagnetics MAS probe. The spectra were obtained using a quadrupole echo pulse sequence, with a 90° pulse length between 2.9 and 4.5 µs using composite pulses34 and phase cycling.35 Interpolation between the free induction decay (FID) data points was used to allow Fourier transformation from the echo maxima, which occasionally was slightly missed by digitization of the FID. Using a MAS probe with a high quality factor for wide-line studies necessarily leads to line shape distortions, especially when the spectra are broad. Insufficient excitation due to long pulses was accounted for in the numerical simulations of the 2H NMR spectra using the program MXQET.36 The syntheses of 2-3,3-d2 and 1-3,3,9,9-d4 are described in the Supporting Information. The compositions of the mixed crystals used in the solid-state NMR experiments were measured with solution-phase 1H NMR using DMSO-d6 as the solvent.

Results and Discussion The ferroelastic behavior of 1/urea is intimately tied to the topological properties of the urea host structure and to the host-guest interactions in this system. With most UICs, the urea molecules are connected by hydrogen bonds to form helical ribbons, which are woven together to form an array of linear, hexagonal tunnels that contain the guest molecules.19 The repeat of the urea helix along the channel axis is reliably 11.0 Å. Although many UICs are nonstoichiometric solids in which the repeats of host and guest are thought to have an incommensurate relation along the channel axis, 1/urea is a commensurate structure18 in which two guest molecules match the repeat of three turns of the urea helix. Through operation of a 2-fold screw along the channel axis, guests adopt an antiferroelectric arrangement in which their mean planes lie roughly parallel to (010), and the CdO groups in adjacent layers lie parallel and antiparallel to [100] (Figure 1). Guests in adjacent channels are tethered through their carbonyls by urea molecules that turn into the channels about their 2-fold axes (Figure 2). This two-dimensional array of guests gives rise to a ferroelastic distortion of approximately 3.7% from metric hexagonal symmetry to give an orthorhombic cell (space group C2221). In the ab plane, the principal component of the strain lies along [100]. Twinning, Epitaxy, and Crystal Growth. As shown below, the ferroelastic domain switching of 1/urea is best understood in the broader context of the twinning and epitaxy observed in this material. Crystals of 1/urea exhibit nonmerohedral rotational twinning across two types of boundaries ({110}{110} and {130}{130}).18,20 These rotational sectors are readily distinguished by their extinction orientations (along {100} and {010}) or their interference colors23 when viewed down the channel axis with a polarizing microscope containing a compensator plate (Figure 3). Although the absolute configuration (i.e. right- or left-handed helix) has not been determined, assignment of domain orientations is


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Figure 3. (a) Photomicrograph (crossed polars, λ plate) of a large crystal grown from a 98:2 mixture of 1 and 2 and urea in methanol. Scale bar: 2 mm. See Figures 13, 16, and 17 for SWBXT images of this crystal. (b) Schematic showing the rotational twins, which have been assigned from their birefringence and their SWBXT images. Arrows represent carbonyl axes for one layer of guest and are parallel to the [100] axis for that domain. (Antiparallel guests are omitted for clarity.) Twinning occurs across two families of boundaries ({130}{130} (blue) and {110}{110} (red)), which are epitaxially matched. Crystal growth occurs through {110} and {010} families of faces, but not through {130} or {100} faces. Figure 1. Channel axis view of 2,10-undecanedione/urea, showing the orientation of applied stress (a axis horizontal, b vertical). Guest molecules are related by a 2-fold screw axis along the channel and are hydrogen-bonded to the host, which adopts a helical structure. This host structure is depicted as a left-handed helix, as defined by the chain of CdO- - -Ha-N hydrogen bonds. Application of stress to a {110} face (see bar at lower right) reorients the guests by approximately 60° (counterclockwise here) in a screw-like motion that moves them to equivalent positions along the helix. Concomitant translation of the guest along the channel ensures a high degree of cooperativity. A (010) slice similar to that highlighted by the yellow rectangle is shown in Figure 2.

Figure 2. Cutaway view of crystal packing of 1/urea ([100] vertical, [001] horizontal) showing the continuous 2-D network of guest-host-guest hydrogen bonds that serves to align the guests in a given domain. Isomorphous substitution of 2 for 1 in mixed UICs interrupts this hydrogen-bonded network and lowers the barrier to domain switching. Note that as one moves left to right, the ureas along a given channel wall alternate in the sense of their tilt with respect to the horizontal plane.

relatively straightforward once it is recognized that macroscopic crystals normally terminate in growth faces belonging to the {110} or {010} families.37 With the understanding that each carbonyl arrow in Figure 3b is accompanied by an antiparallel carbonyl in an

adjacent guest molecule (related by a 21 screw along the channel axis), the observed domain structure in Figure 3a is consistent with twins that are rotated counterclockwise with respect to one another as one moves clockwise around the crystal. As previously demonstrated by the absence of orientation contrast in SWBXT images using the twin composition planes as reflecting planes (and in Figures 16 and 17 below),20 the observed twin-related regions are coincident and are epitaxially matched with each other.38,39 This epitaxy can be understood readily by viewing the two-dimensional projection of the twin boundaries in the ab plane (Figure 4). (The channel axes ([001]) are coincident for each domain; thus, only distortions in this plane are relevant.) For example, with the {130}{130} twins (Figure 4a), the principal component of the strain (see carbonyl arrows along [100]) lies approximately (30° from the twin boundary. The strain or distortion is therefore projected in an equivalent manner from each domain onto the twin boundary, and epitaxy is achieved. Likewise, for {110}{110} boundaries, the [100] axes lie approximately (60° from the twin boundary, and the strain is again projected in an equivalent manner onto the boundary.40 At other boundaries (see Figure 4c,d), the domains are epitaxially mismatched, and growth cannot be sustained. Along the {110}{010} boundary (Figure 4c), for example, the [100] axis of the right domain lies parallel to the twin boundary, whereas that for the left domain lies approximately 60° away from it. In Figure 4d, the angles between the twin boundary and [100] are 90° and approximately 30°. Several other twin boundaries are mismatched and not observed. As described below, mismatched boundaries are implicated in the pseudoelastic behavior observed in these materials. In the polarizing microscope, two other twin boundaries (Figure 4e,f) are “invisible” because the optical indicatrices of these displacive twins are equivalently oriented. Although several types of displacive twins are possible, the simplest of these would involve 180° rotation of the guest and translation by 5.5 Å along the

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Figure 4. Schematic diagrams of twinning and epitaxy in ferroelastic inclusion compounds of 1/urea. For materials that are distorted from orthohexagonal symmetry, such as 1/urea and the mixtures of 1 and 2 in urea described in this paper, rotational twinning is observed across epitaxially matched {130}{130} and {110}{110} boundaries, as shown in (a) and (b). In (a), the {130}{130} boundary is perpendicular to the {110} growth face of the crystal, and the strain on each side of this domain wall (oriented at approximately (30°) is projected onto the boundary in an equivalent manner. (b) Twinning across a {110}{110} boundary. Here, epitaxy is achieved because, on either side, [100] makes an angle of approximately 60° with the twin boundary. (c) Example of an epitaxially mismatched {110}{010} twin boundary in which the strain is projected differently onto the boundary from either side. (d) A {100}{130} boundary that is also mismatched. (e) An “invisible” {100}{100} boundary formed by displacive twins. Here, the guest-host-guest hydrogen bonding network is disrupted at the boundary. (f) An “invisible” {010}{010} displacive twin in which no disruption of hostguest hydrogen bonding occurs.

channel axis. An alternative arrangement in which the guest is simply translated along the channel by 16.5 Å (one guest repeat) is also possible, but this would require the “sense” of tilt for all of the ureas along a given channel wall to change. (See Figure 2 for a description of the alternating orientations of the host molecules.) In principle, both types of displacive disorder are observable as disordered structural models during the full crystal structure determination of 1/urea, but we have found no evidence for this type of displacive twinning in several crystal structures of this material. Although the observed rotational twins are epitaxially matched, birefringence mapping23,33 and strain contrast in SWBXT images20 reveal significant disorder due to loss of guest-host-guest hydrogen bonding at the twin

Hollingsworth et al.

Figure 5. Photomicrograph and birefringence maps (along [001]) of a UIC crystal grown from an 83:17 mixture of 1 and 2 in MeOH (thickness 7.3(2) µm). (a) Photomicrograph using crossed polars and λ plate (scale bar: 50 µm). Individual sectors appear yellow, green, or magenta depending on the orientation of the guest molecules (and [100]) relative to the crossed polars and λ plate. (b) Orientation map (scale bar 43.4 µm). (c) Retardation map for the area enclosed by a box in Figure 5b. Scale bar: 11.6 µm. Note that the retardation is roughly 4-5 times lower in the vicinity of the twin boundaries. Near the nucleation center, where nonadjacent (and epitaxially mismatched) sectors come together, the retardation is quite low, indicating substantial guest disorder. (d) Graph of orientation (red) and retardation (blue) across a {110}{110} boundary at the line section denoted with a “d” in Figure 5c. For five {110}{110} sections, the average apparent width (1.3(3) µm) is at the resolution limit for this microscope. (e) Graph of orientation (red) and retardation (blue) across a {130}{130} boundary at the line section denoted with an “e”. For seven {130}{130} sections, the average apparent width was 0.9(3) µm.

interfaces (Figure 5). In birefringence maps, both {110}{110} and {130}{130} boundaries exhibit significantly lower retardations in line sections traversing these boundaries. This is consistent with the notion that the two-dimensional hydrogen-bonded network aligns the guests and gives rise to the ferroelastic distortion in these materials. The breakdown of these networks at the interface leads to substantial guest disorder and subtle shifts toward hexagonal metric symmetry, which are revealed through strain contrast in SWBXT images that use the twin composition planes as reflecting planes. At the nucleation center of the crystal depicted in Figure 5, nonadjacent (and thus epitaxially mismatched) sectors must come together. The concomitant guest disorder significantly lowers the retardation in this region. (See also Figure 16 below.)


Because the {010}{010} twin boundary (Figure 4f) does not disrupt the host-guest hydrogen-bonding network (which runs parallel to the boundary), this domain wall should show the least amount of local structural distortions and concomitant strain contrast in SWBXT images. The {100}{100} boundaries, on the other hand, can be discerned through dynamical strain contrast in the SWBXT images, since the host-guest hydrogen bonding network is disrupted. (See Figure 16 below.) Although they are known to occur in related UICs of bis(methyl ketones) exhibiting weak birefringence or uniaxial optical properties,23 chiral (Brazil) twins in 1/urea are difficult to discern because the linear birefringence of these biaxial crystals is enormous when compared to the much smaller effect of optical rotation that might allow one to distinguish such twins.41 Our earlier work shows that such twins almost certainly involve nonhelical (stacked loop) host structures that present significant barriers to domain switching and that it should be possible to template right- and left-handed urea helices on either side of the {110} and {010} boundaries.23 To the extent that it occurs in these ferroelastic materials, Brazil twinning should inhibit domain wall motion, so this must be considered in every case.42 Ferroelastic Domain Switching and “Memory Effects”. In 1/urea, ferroelastic domain switching is accomplished by applying uniaxial force to a {110} growth face (Figure 1). To relieve the applied stress, the guests rotate about their long axes by approximately 60°, but the helical topology of the host also requires them to translate along the channel by 1.84 Å to the next available urea molecule that can form a host-guest hydrogen bond. The mechanistic requirement for adjacent guests to move out of each other’s way in this screw-like motion ensures a high degree of cooperativity in this transformation. Because original (mother) and switched (daughter) domains are simply orientation states, ferroelastic domain switching is nominally a degenerate process. For several ferroelastic materials, however, we have observed reversible “memory effects” upon release of the external stress.18,22 Thus, when the coercive force is released, the daughter formed under stress reverts to the orientation of the original mother domain. Until recently,29 such “rubber-like behavior”28 was a longstanding puzzle43-45 in the area of martensitic materials such as shape memory alloys. This phenomenon is to be distinguished from the normal hysteretic behavior observed in ferroic materials, which revert to their original orientation states only once the direction of the coercive force is reversed after the initial switching events. With light forces (e.g. less than 0.5% strain), pure crystals of 1/urea may exhibit reversible (pseudoelastic) domain switching, but larger forces typically give rise to irreversible (plastic) domain switching. However, when UICs grown from an 80:20 mixture of 1 and 2 are subjected to uniaxial stress, the daughter domains invariably retreat to regenerate the mother domain. At higher strains (close to 3%), crystals containing 13-15% of 2 can exhibit either plastic or pseudoelastic behavior. For lower strains (for example, 2.2%), however, mixed crystals almost always exhibit pseudoelasticity and the memory effects described above


Figure 6. Critical threshold behavior for spontaneous reversion of daughter domains as a function of guest composition in the sector undergoing domain switching. Circles denote pseudoelastic or rubber-like behavior, whereas triangles denote irreversible or plastic behavior. Filled symbols denote the first stress of a pristine crystal, gray symbols denote the second stress of the same crystal, and open symbols denote the third, fourth, or fifth stress of a given crystal (six instances of more than three stresses). In one instance (not shown), a sector containing 13.2% 2 exhibited spontaneous reversion after a first stress with an applied strain of 5.3%. Note the dramatic change in behavior for crystals containing 14% or more of 2.

when the sector in question contains more than 14% of 2, but either plastic or pseudoelastic behavior at lower concentrations of 2 (Figure 6). This critical threshold of 14% 2 is indicative of a highly cooperative process in which the disruption of the host-guest hydrogen bonding lowers the barrier to domain switching by reducing the size of the networks that must be reoriented as units at the interface between mother and daughter domains. Because it is tethered to the host on only one end, compound 2 is also more mobile than 1, and, as shown below, this serves to unpin defect sites that hold up the reversion. The observed memory effects surely arise because the crystal growth process creates a more perfect domain than any stress-induced transformation can generate. Thus, the mother and daughter are not truly degenerate, and at the interface between the two domains, the more perfect mother domain can overgrow the less perfect daughter. Acoustomechanical Relaxation. Optical experiments utilizing acoustomechanical vibration provide evidence for differential perfection as a driving force for the observed memory effects. In one experiment, the sector in question contained a 90:10 mixture of 1 and 2 and was shown to exhibit reliable memory effects when forces of 35 cN were applied, even when that force was held in place for 5.5 min (Figure 7a-c,f). Immediately following this treatment, a smaller stress (31 cN) was applied in the same direction and for a shorter time while the stage was vibrated with a small piezoelectric transducer (along the [001] axis of the crystal and perpendicular to the stress; Figure 7d). This acoustomechanical vibration apparently annealed enough metastable defects so that large regions of the daughter did not revert to the original mother orientation upon release of stress (Figure 7e). This acoustomechanical effect may inhibit the domain reversion in two related ways. By facilitating reorienta-

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Figure 7. Acoustomechanical relaxation of daughter domains. (a) Crystal of (90:10 1:2)/urea viewed in the extinguishing position (along [001], [100] horizontal) with crossed polars and a λ plate. Scale bar: 0.5 mm. (b) Generation of daughter domain under 35 cN force along {110} faces (after 5.5 min). (c) Spontaneous reversion to parent orientation after release of stress. (d) Regeneration of slightly smaller daughter under 31 cN force along {110} faces and with 3.0 min of acoustomechanical vibration along [001] at 4.1 kHz (device at 15 V and 1.5 cm from crystal; at 12 V rated at 70 dB (minimum) at 30 cm). (e) Plastic response following (d) and release of stress. (f) Schematic of domain switching in (b) and (d).

tions of the guest, it lowers the energy of the daughter domain by providing more uniform crystal packing within the daughter. This same guest relaxation may also raise the barrier to domain reversion by facilitating reconstruction of hydrogen-bonded networks; this increases the size of the cooperatively linked subunits that must be reoriented together during the reversion process. For crystals containing substantially higher fractions of 2, we have not been able to observe this acoustomechanical effect on the reversion, presumably because the barrier to domain switching is so low that even small amounts of residual strain in the daughter drive the reversion process. With such large fractions of monoketone guest, the host-guest hydrogen-bonding network is already substantially interrupted, so this may also limit the amount by which the barrier can be raised through reconstruction of these networks. A more complete description of acoustomechanical relaxation must be deferred until the nature of the defect sites in the daughter has been discussed. Spontaneous Repair During Crystal Growths A Molecular Earthquake. Videomicroscopy during crystal growth provides striking, macroscopic evidence for the mechanisms by which crystals of 1/urea anneal defects during growth (and therefore become more perfect). In Figure 8a, videomicrographs show the growth of a small crystal of 1/urea over a period of 30 s. In this evaporating methanol solution, turbulent convection generated a moving front of tiny crystallites that flowed from left to right. Just after frame 434, a tiny needlelike crystal (5 × 30 µm, mass approximately 1 ng) traveling approximately 0.5 mm s-1 collided with the yellow sector on the left side of the crystal. A subsequent collision with the top yellow sector is evident in frame 454 (not shown). These collisions coincide with the formation of a circumferential disturbance (see the hexagonal-shaped demarcation on the inner part of the crystal in subsequent frames) and a rotational twinning


event that occurs on the right side of the crystal (readily visible by frame 650, the blue region to the right of the yellow sector). During subsequent growth, this crystal spontaneously undergoes two discernible events that correct structural mismatches associated with the newly formed twin. As described above, rotational twinning in 1/urea is allowed between sectors whose strain is epitaxially matched at their common interface.20 In Figure 8b, the blue and magenta domains share an allowed {130}{130} interface in which the [100] axis of each domain (see arrows) lies approximately +30 and -30° from the twin boundary. Similarly, on either side of the {110}[110} boundary that separates magenta and yellow sectors, the [100] axes are approximately +60 and -60° from the interface. Epitaxy is achieved by coincidence of the projections of the strain from each twin onto the boundary. Following the collision-induced twinning, the newly formed domain (blue in Figure 8c) is epitaxially matched with the inner yellow domain across an allowed {110}{110} boundary (vertical in Figure 8c). Growth of the blue sector cannot easily propagate along the former yellow/red {110}{110} boundary, however, because this epitaxially matched boundary would become a mismatched {010}{110} boundary at the interface between the blue and the magenta domains (cf. Figure 4c). Initially, the blue sector does not form near this boundary (compare frames 550, 650, and 793), but once it does, the former {110}{110} boundary spontaneously changes direction to become an allowed {130}{130} boundary that achieves the necessary epitaxy between blue and the magenta domains (see arrows in frame 793 and Figure 8c). Near the trisection of the magenta, blue, and yellow domains, a local stress develops where the blue domain is adjacent to the magenta domain along a mismatched {010}{110} boundary (Figure 8c). Although the resolution of the video is insufficient for us to determine the spatial extent of the mismatched region (before the twin boundary changes direction), it is apparent that this epitaxially mismatched trisection becomes the epicenter for a spontaneous domain reorientation that relieves the local stress by reorienting large regions of the magenta and yellow domains to that of the blue domain.46 The light blue halo in frame 794 evidently corresponds to a “reaction front” that propagates outward from the mismatched region between the magenta and the blue sectors. (Although the yellow and blue sectors were matched (Figure 8b), the yellow domains must be switched in a secondary event to achieve epitaxy after the magenta domain is switched.) Because the twin boundary exterior to the offending trisection had already reoriented to achieve the requisite epitaxy, the domain switching that occurs in frame 794 bypasses this region altogether (see frames 795 and 899 and Figure 8d). This dramatic example of spontaneous repair during crystal growth shows how local stresses generated at epitaxially mismatched sites can provide the driving force for spontaneous domain switching. But this macroscopic event also highlights the annealing processes that must occur on a molecular level whenever these crystals grow. For crystals exhibiting 12-fold sectoring, disorder is inevitable at the nucleation centers, since nonadjacent sectors are epitaxially mismatched (Figures



Figure 8. Collision-induced twinning during growth of 1/urea from MeOH. (a) Selected frames during growth and twinning (using crossed polarizers and λ plate). Frames are numbered in sequence with each integer separated by 1/30 s. Scale bar: 100 µm. The arrow in frame 434 points to the crystallite that collides with the growing crystal at least twice between frames 434 and 454 and generates a circumferential disturbance during this period (see arrow in frame 650). Note the redirection of the twin boundary (arrow and dashed line) in frame 793. (b-d) Schematics of domain orientations and interference colors. (b) Before the twinning event. Arrows within the channels represent the directions of the guest carbonyl groups and the principal component of strain in the ab plane (the [100] axis). The {130}{130} and {110}{110} twin boundaries are epitaxially matched, because, on either side of the boundary, the projection of the strain onto the domain wall has the same magnitude. (c) After the collisioninduced twinning, the {110}{110} boundary can no longer be sustained because the outer blue domain is no longer epitaxially matched with its magenta neighbor. This twin boundary therefore changes course so that the blue and magenta domains are separated by an epitaxially matched {130}{130} boundary. The white hexagon at the trisection between the magenta, yellow, and blue domains represents the high-energy, mismatched region that becomes the epicenter of the subsequent domain switching event (which relieves this local stress). (d) Here, the blue domain has overtaken the yellow and magenta sectors to leave behind epitaxially matched boundaries. W A video of spontaneous domain switching during crystal growth in QuickTime format is available.

3b and 5). This disorder is readily apparent in birefringence maps, where it is manifested as regions of low retardation that are typically several micrometers wide, and in SWBXT images (as in Figure 16 below). Generation of the highly ordered sectors that emerge from these chaotic nucleation centers can be accomplished quite readily by reorientation and alignment of guest molecules. Once the ferroelastic distortion becomes large enough (i.e. further from the nucleation center), relief of strain at dislocations occurs through twinning processes that follow the rules of epitaxy outlined in Figure 4 above. Kinetics of Domain Switching and Pinned Sites. The domain switching event observed in frame 794 of the crystal growth video is an excellent example of the

delayed response that is often observed during spontaneous reversion of daughter domains that have been generated with external force. Although stress-induced defect sites in the daughter (see below) are thought to drive the spontaneous reversion to the mother orientation, other regions within the daughter may serve as “pinned sites” that inhibit domain wall reversion. The kinetic studies described here indicate that 2 lowers the barrier to domain reversion principally by relaxing pinned sites generated by the applied stress. To understand the role of impurities in the spontaneous reversion process, we used ultrafast videomicroscopy to document the domain wall motions in a series of mixed UIC crystals containing 1 and 4.7-17.6% of 2. Earlier work using a camera operating at 1000 fps

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Figure 9. Ultrafast videomicroscopy images showing stepwise domain reversion in a crystal of (84.2:15.8 1:2)/urea after compression to 1.38% strain. (This is the third stress of the crystal used for entry 10 of Table 1.) (a) Schematic showing domain orientations of mother (dark and extinguished), daughter (light strips between mother domains), and {110} twin (light region in lower left section of the crystal), as well as the orientation of the active stress bar. Scale bar: 500 µm. Frames b-o show every 20th frame (2.0 ms) in a sequence collected with an X-StreamVision XS-4 ultrafast video camera operating at 10 000 fps. The numbers in the upper right corners of the frames correspond to the times in ms. The stress bar was released between frames b and c at 5.4 ms. Because of unavoidable crystal motion, which moves transmitting regions of the crystal in and out of the frame, frames c-e were not included in this analysis, which starts at frame f (12 ms). The box in frame f shows the initial position for the integration window.47 W A video of domain reversion at 10 000 fps in QuickTime format is available.

showed that this frame rate was insufficient for most crystals, but it is possible to collect meaningful data at 3000-10 000 fps. The sequence of images for a UIC containing an 84.2:15.8 mixture of 1 and 2 (Figure 9) highlights the typical behavior of these materials as well as some of the difficulties of these experiments. After application of stress, the active stress anvil is retracted at a rate that is much faster than the domain switching process itself. Even if a thin film of oil is used to hold the crystal in place, crystal motion is unavoidable, and some sequences are compromised because the motion

blurs the images or moves the region of interest in and out of the field of view. In the sequence shown in Figure 9, the anvil was removed between (b) and (c) at time ) 5.4 ms. Unfortunately, the upper left portion of the region undergoing domain switching moved in and out of the video frame during the first 6 ms; therefore, the analysis was not started until time ) 12 ms (frame f). As shown in Table 1, the fastest reversion rates are often observed within the first few frames following release of the stress bar. It is therefore inappropriate to compare video sequences that have large delays



Table 1. Summary of Ferroelastic Domain Reversion Kinetics in Mixed UICs Containing 1 and 2 entry no. 1 2 3 4 5 6 7 8 9 10 11 12

amt of 2 (%)

strain (%)

capture rate (fps)

dwell time (ms)

event length (ms)

frames sampled

fastest rate (mol s-1)

slowest rate (mol s-1)

delay to fastest rate (ms)

4.7 10.8 11.3 11.4 11.5 11.8 12.5 15.0 15.0 15.8 17.0 17.6

0.76 0.90 0.90 0.85 0.44 1.21 2.12 1.96 1.96 0.68 1.05 1.05

1000 3000 500 3000 3000 3000 5000 5000 5000 5000 5000 5000

1 0 0 0 0 0 0 0 0 0 0 0

254 2.7 10.0 7.3 26.3 39.0 1380 3.0 101.4 2.4 246 22.6

255 9 6 23 80 118 105 16 198 13 124 114

1.41 × 10-8 9.29 × 10-8 6.20 × 10-9 3.22 × 10-7 1.34 × 10-7 3.80 × 10-8 6.10 × 10-10 1.10 × 10-8 1.64 × 10-8 4.37 × 10-8 6.37 × 10-8 6.37 × 10-8

1.36 × 10-11 1.45 × 10-11 4.08 × 10-10 1.77 × 10-9 1.61 × 10-10 5.14 × 10-10 5.44 × 10-12 6.18 × 10-10 2.58 × 10-11 2.62 × 10-10 2.90 × 10-9 2.27 × 10-10

250 0 2.0 0 24 2.7 5 2.4 2.4 1.6 0 0.4

between anvil release and the initiation of measurements (such as this one) with those in which the events could be measured immediately after anvil release. Nevertheless, the sequence shown in Figure 9 is illustrative of the stepwise kinetics that we have observed in all of the crystals in this series and in pure crystals of 1/urea. Within the active integration window (Figure 9f), the daughter domains appear as light stripes between extinguished mother domains (cf. schematic in Figure 9a). Of the three main daughter regions, the uppermost one is the first to disappear (by frame k). The other two daughter regions decay slowly throughout most of the sequence, but then disappear rapidly between frames n and o. This stepwise decay is summarized in Figure 10, which shows at least three (and as many as five) regions of linear decay. Table 1 summarizes the kinetic data for 12 crystals containing 4.7-17.6% of 2. Instantaneous rates were tabulated by measuring the differences in guest concentration for each pair of adjacent frames throughout a given sequence. For most of the experiments, all of the video frames were analyzed. However, in three of the entries, the event spanned too many frames for each to be sampled, so the sampling frequency was decreased. For entry 7, every 25th frame was analyzed; for entry 9, every 3rd frame was analyzed; for entry 11, every 10th frame was analyzed. Although the reversion kinetics were studied for dozens of crystals, it is most useful to compare those in which the delay between anvil

Figure 10. Kinetics of spontaneous reversion of daughters in (84.2:15.8 1:2)/urea after compression to 1.38% strain. Using the size of the integration box and the thickness of the crystal, luminosities were converted to moles (of guest) remaining in the daughter orientation. Black squares represent frames f-o (at 20 frame intervals between 12 and 30 ms) in Figure 9. In three regions of linear decay, the rates (from left to right) were 2.76 × 10-8, 3.48 × 10-9, and 1.15 × 10-7 mol s-1.

release and the first kinetic measurement (the dwell time) was minimal or zero. In Table 1, the dwell time was zero for all but one of the kinetic runs (entry 1). For entry 1, the fastest instantaneous rate occurred 250 ms after the anvil release, so this is safely included, even though the dwell time is nonzero. We have found that repeated stress of a crystal can slow the fastest reversion rates (presumably because pinned defect sites are accumulated); thus, we include here only pristine (uncut) crystals that were stressed for the first time. Of the 12 mixed crystals containing 4.7-17.6% of 2, 9 were compressed to strains of 0.44-1.2% whereas 3 others (entries 7-9) were compressed to strains of 1.962.12%. In every case, we observed stepwise kinetics for domain reversion, indicating a distribution of barrier heights. For the 9 crystals initially stressed to 0.441.2%, the measured rates for domain switching spanned a range of approximately 24 000, but the instantaneous rates measured for the fastest sites varied by only a factor of 52 over this composition range (6.2 × 10-9 to 3.2 × 10-7 moles of guest s-1), and they showed no correlation with concentration of the relaxive impurity (2). Although we had anticipated otherwise, the rates of the fastest sites (but not the plastic to elastic threshold) appear to be independent of composition; therefore, we must conclude that 2 facilitates spontaneous domain reversion by relaxing pinned sites that present barriers to domain wall motion. Thus, the memory effects are observable because the reversion of slow sites (which are immeasurably slow in plastically switched crystals) is allowed by this relaxive impurity. These findings are summarized in Figure 11, in which instantaneous rates were binned over half log units. The crystal containing 12.5% of 2 (entry 7) was compressed by 2.12% and had a fastest rate that was 528 times slower than that observed for crystals initially compressed to lower strains. This system also had the slowest measured rate and extends the range of rates to a factor of 59 200. Although the limited sample size indicates that further work is required at such high strains, these anomalously low rates may indicate that there is an accumulation of pinned defect sites (which raise the barrier), that the system has surmounted a higher barrier, or that the system has achieved a more stable daughter structure. All three are plausible. Solid-State NMR of Guest Motions. Clues to the guest dynamics and the role of relaxive impurities may be obtained from solid-state 2H NMR spectra (Figure 12), which reveal a surprising amount of guest motion about the channel axis in this system. At 295 K, the 2H

2110


Figure 11. Distributions of measured instantaneous rates for crystals of (1 + 2)/urea containing different amounts of 2. The vertical axis represents the percentage of the daughter that reverts within a given range of rates (with binning over half log units). For each composition, the percent strain is given in the lowest box; the three runs at higher strains are highlighted in red.

Figure 12. Experimental 2H NMR spectra (46.06 MHz) of 1-3,3,9,9-d4/urea, 2-3,3-d2/urea and mixed crystals of 1-3,3,9,9d4/urea containing various amounts of 2 and simulated spectra assuming the jump model described in the text (θ ) 90°, φ ) 30° for a-c and 60° for d): (a) 1-3,3,9,9-d4/urea fit with 53% at the major site (QCC ) 78 kHz); (b) 77% 1-3,3,9,9-d4, 23% 2 in urea fit with 50% at the major site (QCC ) 77 kHz); (c) 46% 1-3,3,9,9-d4, 54% 2 in urea fit with 41% at the major site (QCC ) 82 kHz); (d) 2-3,3-d2/urea fit with equal populations at three sites separated by φ ) 60° (QCC ) 76 kHz).

NMR spectra of 1-3,3,9,9-d4/urea reveal that the guests are in the fast-motion limit (τ e 10-7 s), and they can be simulated quite well36 by assuming jumps about the channel axis between sites that are (30° from the equilibrium position shown in Figure 12. Because the C-D bonds are orthogonal to the channel axis and the jump model involves rotation about that same axis, the C-D bonds lie in a plane throughout the motion; thus, the opening angle (θ) for the cone describing the motion is 90°. These spectra are in the fast-motion limit; therefore, the 30° jumps used in our model cannot be distinguished from other jump angles (for example, 60°).48,49 Currently, we favor an angle of 30° because of the free space available at the vertices of the channels.


Figure 13. Central region of a transmission mode SWBXT image (80% of actual size) of the UIC crystal grown from a 98:2 mixture of 1 and 2 in methanol and depicted in Figure 3. Figures 16 and 17 show expansions of the regions denoted by arrows a and b.

Unless it is coupled to a translation to the next urea position along the helix, a 60° jump to an adjacent channel wall should move the guest to a potential energy maximum.50 Assuming the jump angle φ ) 30° (θ ) 90°) and a pseudosymmetric potential surface, the 2H NMR spectra indicate that the guest molecules spend only 53% of their time at the unique site depicted in Figure 1 (and, according to the model, that they divide their remaining time equally between the other two sites). The 2H NMR spectra of UICs of 1-3,3,9,9-d4 grown in the presence of 2 verify that the alkanedione guests spend even less time in the lowest energy position as the concentration of 2 is increased, but the change in population of this unique site (12% reduction for a 54% increase in the concentration of 2) is less dramatic than one might have expected for such large concentrations of 2-undecanone. This, however, fits well with our kinetic data on domain reversion, in which the intrinsic (maximal) rate of domain reversion did not change significantly as the concentration of 2 was increased. Although not strictly comparable (because crystals of 2/urea are metrically hexagonal and incommensurate along the channel axis),18,51 our spectra of pure 2-3,3-d2/urea (Figure 12d) exhibit dramatically attenuated quadrupole splittings that require jumps with apparent symmetry equal to or larger than 3 (most likely 60° in this hexagonal channel). We anticipate that spectra of 2-3,3-d2 mixed with various amounts of 1 in urea will demonstrate that monoketone 2 has much greater mobility than diketone 1 in crystals containing the same ratio of 1 and 2. The present data leave no doubt, however, that 2 can act as a relaxive impurity, and this is consistent with other instances in which host-guest hydrogen bonding can dramatically change the dynamics of a guest.52 Synchrotron White Beam X-ray Topography (SWBXT). Synchrotron white beam X-ray topography (SWBXT)20,31,53 is currently one of the most powerful methods for investigating the defect structures and symmetry of twinned and disordered crystals. To explore the details of differential perfection in mother and daughter domains, we conducted in situ stress experi-



Figure 14. Transmission mode SWBXT images and photomicrograph of mixed crystals of 1 and 2 in urea. (a-c) Crystal grown from 98:2 1:2/urea. (a) Before stress. (b) Under 58 cN horizontal force. (c) After release of stress. No discernible pattern emerges for plastically switched daughters. (d-f) 84:16 1:2/urea. (d) Before stress (inset m is the (2 h 43) reflection). Note the fine horizontal striations, which indicate nanoscopic twins along {130}. (e) Under 90 cN horizontal force. (f) After release of stress, showing primarily pseudoelastic response. The expanded region in (n) highlights the subtle changes after release of stress. (Note the overall increased contrast of the horizontal striations and the newly oriented striations near the red arrows.) (g-l) 89:11 1:2/ urea. (g) Before stress. (h) Under 63 cN horizontal force. Thin strips labeled 1 and 2 arise from daughters generated in the dark sector directly above them. (i) After release of 63 cN force. Note the relatively undistorted daughters in the box (inset (o)). (j) After stress (112 cN force) and release. (k) Photomicrograph after stress (crossed polars in directions shown with arrows, λ plate). (l) Schematic showing daughters 1 and 2. Note that, with respect to the external stress, daughter 2 is degenerate with the mother and was therefore unanticipated. Its growth is consistent with the preexistence of {130} twins that merge in order to minimize their surface area in contact with “normal” daughters generated by the stress, and, in 86:14 1:2/urea, with the increased dynamical contrast exhibited in the n versus m. In a-k, scale bars (shown only in (a) and (k)) are 2 mm. Scale bars in m-o are 0.5 mm.

ments on mixtures of 1 and 2 in urea, in which we collected alternate images using SWBXT and videomicroscopy with the sample between crossed polars. Crystals were held with their (001) plate faces nearly perpendicular to the highly collimated X-ray beam and briefly exposed in transmission mode to reveal the Laue spots for the most intense reflections. In this white beam

experiment, differently oriented sectors meet the Bragg condition at different wavelengths and angles; therefore, the Laue pattern for a sectored crystal appears as exploded clusters of images in which each image corresponds to a particular Miller plane and in which opposite sectors appear in pairs (Figure 13). This technique is exquisitely sensitive to strain, which may

2112


Figure 15. Schematic potential energy surface for domain switching, showing effects of relaxive impurities and acoustomechanical vibrations.

be manifested as either a distortion in the images for larger strains or significant dislocations54 or as dynamical diffraction contrast31 for more subtle imperfections, including nonuniform strain and mosaicity. In these experiments, crystals of 1/urea (and others containing 2-12% 2) exhibited the plastic response that had been expected from our optical studies. Under stress, the SWBXT images were spread out to more than twice their original size, and no discernible pattern emerged upon release of the stress (Figure 14a-c), although optical micrographs demonstrated that daughter domains had been formed. Above the critical impurity threshold, however, the response was highly elastic. For a crystal of 84:16 1:2/urea, application of force again spread the pattern out by more than a factor of 2, suggesting significant levels of strain and dislocations (Figure 14d,e,m). Upon release of the stress (Figure 14f), pseudoelastic domain reorientation was almost complete, and the SWBXT pattern reverted to a relatively undistorted one that differed from the original primarily in the extent of dynamical diffraction contrast (cf. Figure 14m,n). Topographs of a crystal containing an 89:11 mixture of 1 and 2 proved to be the most revealing. In this crystal, two different kinds of irreversibly formed daughter domains (see below) diffracted as single crystals that did not show excessive damage upon removal of the stress (Figure 14g-l,o). After release of higher levels of force, some damage was evident in the topographs, but these regions showed much less distortion than in equivalently treated samples containing smaller amounts of 2. Here the concentration of relaxive impurities is low enough to give a plastic response but high enough to anneal the local strain and dislocations that would otherwise broaden and distort the topograph. At lower impurity concentrations, barriers to molecular motion are high enough so that the stress-induced domain switching gives rise to irreversibly formed dislocations and metastable sites in the daughter that are not annealed. In crystals containing higher concentrations of 2, the relaxive impurity apparently lowers the barrier to domain switching (for these slow sites) more than it lowers the energy of the daughter. The effects of the relaxive impurity and acoustomechanical vibrations on the potential energy surface for domain switching are summarized in Figure 15. Relative to the pure crystal, both mother and daughter are raised in mixed crystals of 1 and 2 because of the loss


of hydrogen bond acceptors. Stressed defects generated in the daughter during domain switching raise its energy relative to the mother and drive the spontaneous reversion. (Although both relaxive impurities and acoustomechanical vibrations also affect the mother domain, these effects are thought to be smaller than in the daughter, where stressed defect sites dominate the energetics.) As shown with SWBXT (Figure 14o), the relaxive impurity can anneal strain generated at defects in the daughter. The pseudoelastic response at higher concentrations of 2 shows that this relaxive impurity lowers the barrier more than it stabilizes the daughter. (By decreasing the size of cooperatively linked units that must be switched together, this impurity decreases the barrier to reversion.) However, the kinetic studies show that this impurity functions mainly to accelerate the slow sites instead of raising the intrinsic reversion rate. The acoustomechanical vibrations may raise the barrier and lower the daughter through relaxation (and thus alignment) of disordered or misoriented regions. Nanoscopic Twins Revealed with SWBXT. Although more than one type of defect may be present, fine striations in the topographs of the mother domains are consistent with the occurrence of minute amounts of several types of nanoscopic twins that are epitaxially matched (and can therefore coexist39) with the surrounding mother domains. As discussed above, slight changes in unit cell constants are expected at these twin boundaries because of the absence of bridging guesthost-guest hydrogen bonds between neighboring channels.18,23 Such subtle imperfections do not shift the SWBXT patterns appreciably, but differences in primary extinction of the X-ray beam lead to dynamical diffraction contrast31 that is most prominent along the g vector, which bisects the incoming and diffracted beams. For the cluster of SWBXT images shown in Figure 16, we assign the dynamic diffraction fringes by making only one assumption, which is that the nanoscopic twins must be epitaxially matched with their surroundings.55 These assignments are supported by the much more prominent strain contrast in a different region of the same topograph in which these line defects lie along the g vector (Figure 17). The nanoscopic twins are too small to give coherent diffraction images (which would appear as ghost images in different parts of the Laue pattern); thus, they may be as narrow as a few hundred angstroms or less. Although we often observe macroscopic twins with these materials, the twins revealed by dynamical diffraction contrast are invisible to ordinary light microscopy (cf. Figure 3). Given the birefringence data discussed above (Figure 5), they most likely exhibit substantial disorder, but we have depicted them as idealized twins in Figure 16 and elsewhere in this paper. Mechanistic Implications of Nanoscopic Twinning. Although differential perfection between mother and daughter domains almost certainly gives rise to the spontaneous reversion or “rubber-like” behavior, a truly perfect mother domain should undergo an irreversible (plastic) domain switching process to a perfect daughter that exhibits no memory effects. On the other hand, a less than perfect mother containing numerous epitaxially matched twins of the sort shown in Figure 16 can generate an unstable daughter containing epitaxially



Figure 16. Expansion of the SWBXT image in Figure 13 (see arrow a) showing dynamical strain contrast along line sections parallel to lamellar twins with proposed assignments shown in the schematic diagrams. Note the subtle curvature of the sectors near the nucleation center and substantial loss of intensity at that site. Both effects indicate strain and/or disorder at the nucleation center.

mismatched twins in the domain switching process (Figure 18). Ferroelastic domain switching is a cooperative process that involves screw-type motions of the guests along the channel; to the extent that the guest motions in these nanoscopic twins are uncoupled from those in the surrounding mother domains, these twins become mismatched with the daughter upon application of stress (Figure 19B). (Indeed, stress-induced growth of such twins (Figure 14h-l) was considered anomalous until it was realized that merging these twins could minimize the surface area of mismatched boundaries.) A conceivable “least motion” process that relaxes the stress on these twins involves an energetically feasible screw-like motion of guests in the opposite direction along the channel to generate an “allowed” twin (Figure 19C). Complete relaxation of this twin (so that it is aligned with the daughter) would require 180° rotation and 5.5 Å translation of the guests along the channel axis (Figure 19D). Such large translations of 5.5 Å have precedent in phase transitions of other ferroelastic UICs;21 thus, it is conceivable that acoustomechanical vibrations directed along the channel axis of compressed crystals could re-

Figure 17. Central portion of a cluster of images in the same topograph (see arrow b in Figure 13). Because the g vector is coincident with the striations, they exhibit greater strain contrast than in Figure 16. Note the subtle strain contrast across vertical {110}{110} twin boundaries in the sectors whose topographs are coincident (and thus merged) at the top and bottom of this image. This is also present along analogous {130}{130} boundaries in Figure 16.

2114


Figure 18. Memory effects in ferroelastic UICs. A truly perfect mother domain (a) should generate a degenerate daughter (b), and no memory effects should be observed. A mother domain that is filled with epitaxially matched, nanoscopic twins (c), however, generates a mismatched daughter (d) and leads to spontaneous reversion.

Figure 19. Plausible mechanistic scheme for memory effects and acoustomechanical relaxation of the daughter. Potential energy minima and barriers are approximate and do not reflect the bias of external compression. Under stress, the mother (A), which contains epitaxially matched twin defects, generates a metastable daughter (B) containing mismatched sites via clockwise rotation of guests along the urea helix. Further stress aligns the mismatched, nanoscopic twins with their surroundings (C) in a counterclockwise guest reorientation that ultimately displaces these guests from their counterparts by 5.5 Å along the channel. Under stress, acoustomechanical vibration can conceivably drive the rotational-translation motion of the guests along the channel axis over the higher barrier to (D), thus relaxing the daughter.

lax the daughter by surmounting the barrier between C and D in Figure 19. Under external compression, the energies of A and B are raised relative to C and D, so reversion to these states becomes more difficult.56 Although further work is required, in situ stress experiments on a single-crystal diffractometer implicate the nanoscopic twins shown in Figure 19A (or Figure 19B) in the domain switching process. In such experiments, which will be reported elsewhere, reflections from all three domain orientations represented in Figure 19 can be observed and indexed for a UIC crystal grown from a 92:8 mixture of 1 and 2. With small uniaxial compression (approximately 2% strain, 22 cN), the nanoscopic twins (oriented as shown in Figure 19A or Figure 19B) initially increase in size (presumably by merging) until their diffraction patterns appear along with those of the daughter. (Although the orientation of these twins is known, their surroundings (i.e. mother or daughter) and the orientation of their twin boundaries cannot be determined in this experiment. Our depiction in Figure 19 is consistent with the optical micrograph and schematic shown in Figure 14k,l. It also


comports with the increased dynamical diffraction contrast observed in Figure 14n (versus Figure 14m) after pseudoelastic reversion.) This process should be facilitated because it reduces the surface area of the mismatched interfaces with the surrounding daughter. As the strain is increased from 2% to 4% (42 cN), these merged twins are converted to daughter. Release of the external stress increases the intensity of reflections corresponding to the twin shown in Figure 19A in this crystal, which exhibited both plastic and pseudoelastic behavior. Quite significantly, a post mortem evaluation with optical microscopy provided no evidence for the twin shown in Figure 19A, showing that the concentration and/or spatial extent of such twins is low even after stress-induced merging. Broader Implications. Recent work has shown that in metal alloys that exhibit rubber-like behavior and in perovskite ferroelectrics that exhibit “aging-induced microstructure memory”, the process of aging or annealing after cooling through a symmetry-lowering phase transition allows point defects to conform to the crystal symmetry of the parent, thus providing a bias for the observed memory effects.29,57-61 Although the relative merits of interfacial effects and “volume” effects were debated for decades,27,28,45,62,63 the work of Ren and co-workers29,43,60,61 shows that rubber-like behavior in shape memory alloys and memory effects in the perovskite ferroelectrics are essentially volume effects, because the symmetry conforming point defects are distributed widely and are not concentrated at twin boundaries. In the current system of (1 + 2)/urea, the ubiquitous presence of nanoscopic twins and the direct diffraction evidence for merging them strongly favors an interfacial origin for rubber-like behavior at modest strains (e.g. 2%). At higher strains (e.g. 3%), where these twins are aligned with the daughters, the bias that drives the reversion is evidently smaller since both mother and daughter (Figure 19A and Figure 19C) are lacking similar numbers of guest-host-guest hydrogen bonds. (Note the plastic behavior of crystals above the critical threshold at strains of 3% in Figure 6.) At these higher strain levels, the distinction between interfacial effects and volumetric effects is blurred because the displacive regions (Figure 19C) arising from the nanoscopic twins are dispersed throughout these crystals and are merohedrally aligned with the daughter. Our full crystal structures (at -150 °C) of unswitched and plastically switched regions of the same crystal sector containing a 92:8 mixture of 1 and 2 showed no significant structural differences and only minor increases in the isotropic displacement parameters for host and guest molecules in the plastically switched crystal. In the two unpublished crystal structures of plastically switched crystals that we have completed thus far, disordered models show no significant refined occupancy for the displacive guest site depicted in Figure 19C. This reinforces the notion that these nanoscopic twins, although distributed throughout the crystal, occupy only a tiny fraction of the crystal volume. They are, after all, typically invisible to ordinary light microscopy. Because it lacks a hydrogen bond acceptor at one end, 2 tends to promote disorder and twinning during crystal


growth.18 One might therefore argue that the critical threshold behavior exhibited for mixtures of 1 and 2 in urea is simply a consequence of the increased frequency of nanoscopic twins formed during crystal growth from solutions containing larger amounts of 2 and the concomitant bias against daughters containing these mismatched twins. Related arguments based on groundstate destabilization of the daughter are central to mechanisms involving rubber-like behavior and memory effects in the systems described by Ren,29,61 where volume effects appear to predominate. Crystals grown from 98:2 mixtures of 1 and 2 (Figures 13, 16, and 17) are filled with nanoscopic twins, however, and for the materials that we have studied thus far with SXBXT, there does not appear to be a correlation between dynamical diffraction contrast (from nanoscopic twins) and the concentration of 2 (up to 18% of 2). Although SWBXT provides only a qualitative assessment of nanoscopic twinning, this suggests that the bias against the daughter should exist both above and below the critical threshold. SWBXT (Figure 14i,o) shows furthermore that increasing the amount of 2 can actually anneal those sites whose strains are mismatched with their surroundings in the switched crystal. It therefore seems likely that spontaneous reversion is observed above the critical threshold because pinned sites that hold up the domain reversion are effectively relaxed by the relaxive monoketone impurity. However, to the extent that the pinned sites that hold up the reversion are merely “perfect” daughter regions represented by Figure 19D, the concentration of 2 could play a role in reducing their size and the cohesive forces holding them together. Ultrafast kinetic studies of crystals that are prescreened with SWBXT should provide further insights into the stepwise nature of domain reversion and the rubber-like behavior exhibited by these crystals. The dual role for defect sites in either driving the reversion or pinning domain wall motion is highly reminiscent of the work of McBride and co-workers on solid-state photoreactions, where it was shown that the accumulation of photochemically generated defects can either accelerate or retard subsequent reactions.7,10,64 In related work, it was shown that relaxive impurities can again either accelerate or retard reactions that are controlled by photochemically generated stress.9,10 In a sense, ferroelastic domain switching is a prototypical solid-state reaction, so one might expect such a close correspondence in the factors that control both chemical and physical processes in the solid state. The molecular inclusion compounds that we have described here are structurally much more complicated than the shape memory alloys and perovskite ferroelectrics that exhibit rubber-like behavior and memory effects. This molecular complexity leads to a more intricate potential energy surface for domain switching and relaxation, but it also provides numerous opportunities for probing these pathways that are unavailable for simpler materials such as alloys. In all cases, however, the underlying mechanisms are similar in that an “imperfectly perfect” parent domain or phase appears to provide the bias against formation of the daughter. One important difference is that, in the channel inclusion compounds, mechanisms exist during crystal growth to generate epitaxially matched defects


within the parent, as revealed by the video sequence outlined in Figure 8. The same kinds of interfacial interactions that give rise to the delayed switching event depicted in Frame 794 of Figure 8a are thought to drive the spontaneous domain reversion in mixed crystals of 1 and 2 in urea. Our studies of related and unrelated ferroelastic and ferroelectric inclusion compounds suggest that the memory effects and pseudoelasticity described here could be quite general; control of twinning65 and specific tailoring of cooperative, elastic barriers should therefore be important considerations for the generation of useful ferroic materials. Acknowledgment. We thank T. A. Geiger, G. A. Crundwell, B. Kahr, C. A. Schertz, K. E. Nicolaysen, and G. Dhanaraj for their help with this work, C. T. Culbertson for the use of his HPLC, and Speed Vision Technologies for the use of their ultrafast video camera. This work was supported by the U.S. National Science Foundation (Grant Nos. DMR-9996243, CHE-0096157, and CHE-0097411), the NASA Microgravity Materials Science Initiative (Grant No. NAG8-1702), the U.S. DOE, Research Corp., and unrestricted grants from Pharmascience, Inc. and Apotex, Inc. Note Added after ASAP Publication. An earlier version of this paper posted ASAP on the Web on October 12, 2005, contained incorrect data in Table 1 and on lines 719 and 723, and an incorrect Figure 11. These data have been corrected, and a new sentence on line 705 has been added, in this new version of the paper posted October 20, 2005. Supporting Information Available: QuickTime videos of spontaneous domain switching during crystal growth (Figure 8) and of domain reversion at 10 000 fps (Figure 9) are provided, as are text and figures giving details of the experiment showing acoustomechanical relaxation of the daughter and experimental procedures for the preparation of deuteriumlabeled guests. This material is available free of charge via the Internet at http://pubs.acs.org.

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Hollingsworth et al. (43) (44) (45) (46)

(47)

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Otsuka, K.; Ren, X. Scr. Mater. 2003, 50, 207-212. O ¨ lander, A. J. Am. Chem. Soc. 1932, 54, 3819-33. Zangwill, A.; Bruinsma, R. Phys. Rev. Lett. 1984, 53, 1073-6. This series of events suggests an alternative definition for the term “molecular tectonics”! It is also a striking manifestation of the chemical pressure model. See: Luty, T.; Eckhardt, C. J. J. Am. Chem. Soc. 1995, 117, 2441-2452. The position of the integration box in Figure 9f was adjusted in subsequent frames (by as much as 4 pixels in x and y) according to landmarks on the crystal. Although the upper left corner of the integration window moved in and out of the video frame, this region of the crystal remained extinguished and therefore did not affect this analysis. The tops of the images were cropped for display in this figure. Hollingsworth, M. D.; Werner-Zwanziger, U.; Brown, M. E.; Chaney, J. D.; Huffman, J. C.; Harris, K. D. M.; Smart, S. P. J. Am. Chem. Soc. 1999, 121, 9732-9733. Werner-Zwanziger, U.; Brown, M. E.; Chaney, J. D.; Still, E. J.; Hollingsworth, M. D. Appl. Magn. Reson. 1999, 17, 265-281. Lauritzen, J. I., Jr. J. Chem. Phys. 1958, 28, 118-131. Hollingsworth, M. D.; Brown, M. E.; Hillier, A. C.; Santarsiero, B. D.; Chaney, J. D. Science (Washington,D.C.) 1996, 273, 1355-1359. Hollingsworth, M. D.; Santarsiero, B. D.; Harris, K. D. M. Angew. Chem., Int. Ed. Engl. 1994, 33, 649-652. Hollingsworth, M. D.; Brown, M. E.; Dudley, M.; Chung, H.; Peterson, M. L.; Hillier, A. C. Angew. Chem., Int. Ed. 2002, 41, 965-969. Ristic, R. I.; Sherwood, J. N.; Wojciechowski, K. J. Cryst. Growth 1988, 91, 163-8. The occurrence of Brazil twins along {130} or {100} boundaries cannot be accommodated by simple structural models that template right and left-handed helices (as it can along {110} boundaries). We therefore disfavor Brazil twinning, which we observe only infrequently in related UICs, as the source of the dynamical diffraction contrast observed here. Its infrequent occurrence also argues against its importance in the ubiquitous memory effects. In the absence of compressive stress, acoustomechanical vibration of the crystal depicted in Figure 14j,k showed no discernible changes in its SWBXT patterns. According to the mechanism depicted in Figure 19, analogous experiments with crystals under stress should give SWBXT images that are influenced by this acoustomechanical relaxation process. Tsuchiya, K.; Tateyama, K.; Sugino, K.; Marukawa, K. Scr. Metall. Mater. 1995, 32, 259-264. Marukawa, K.; Tsuchiya, K. Scr. Metall. Mater. 1995, 32, 77-82. Cahn, R. W. Nature (London) 1995, 374, 120. Ren, X.; Otsuka, K. Phys. Rev. Lett. 2000, 85, 10161019. Ren, X. Nature Mater. 2004, 3, 91-94. Cahn, J. W. Acta Metall. 1977, 25, 1021-1026. Lieberman, D. S.; Schmerling, M. A.; Karz, R. W. In Shape Memory Effects in Alloys; Perkins, J., Ed.; Plenum: New York, 1975; pp 203-244. Whitsel, B. L. Ph.D. Thesis, Yale University, New Haven, CT, 1977. Fousek, J.; Cross, L. E. Ferroelectrics 2003, 293, 43-60.

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Memory and Perfection in Ferroelastic Inclusion Compounds - Crystal

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