Supercolossal Uniaxial Negative Thermal Expansion in Chloranilic Acid Pyrazine, CA-Pyz

: There has been signi ﬁ cant recent interest in exploiting the large dimension changes that can occur in molecular materials as a function of temperature, stress, or under optical illumination. Here, we report the remarkable thermal expansion properties of chloranilic acid pyrazine co-crystals. We show that the compound shows uniaxial negative thermal expansion over a wide temperature range with a linear contraction coe ﬃ cient as low as ( − )1500 × 10 − 6 K − 1 at 250 K. The corresponding 10% contraction between 200 and 300 K is an order of magnitude larger than in the so-called colossal contraction materials. We adopt a symmetry-inspired approach to describe both the structural changes that occur (using rotational symmetry modes) and the thermal expansion (using strain modes). This allows an extremely compact description of the phase transition responsible for this unusual behavior and gives detailed understanding of its atomic origins. We show how the coupling of primary and secondary strain modes in materials showing extreme expansion and contraction can lead to unusual reversals in the temperature dependence of cell parameters.


■ INTRODUCTION
There has been significant interest in the physical properties of crystalline organic and hybrid materials in recent years, particularly in some of the mechanical properties traditionally studied in metallic, ceramic, and polymer engineering materials. 1, 2 The weaker bonding interactions present between organic molecules often enhance the magnitude of important properties, and their design-flexibility makes them a rich arena for discovery. Much of the interest in the field is driven by the possibility of creating stimulus-responsive materials that display macroscopic changes and can act as actuators or artificial muscles. 3−5 For example, there has been a number of reports over the years of "bending crystals", which undergo dramatic shape changes either on heating or on the application of mechanical stress, some of which have been recently reviewed. 3,4 This behavior is usually linked to the evolution of twin structures associated with phase transitions and, as such, closely related to the phenomena that lead to effects such as shape memory and superelasticity in metal alloys like nitinol. There has, therefore, been significant interest in martensite-like transitions in organic crystals; 6−12 recent examples of materials exploiting these include the superelastic terephthalamide 13 and the organic shape memory material (P n Bu 4 ) + (BPh 4 ) − . 14 Mechanical twinning leads to effects such as ferroelasticity and superelasticity, and a number of molecular systems have been reported with this property. 15−21 Finally, N,N-dimethyl-4-nitroaniline crystals have recently been shown to display superplasticity. 22 Herbstein provides a useful overview of the mechanism of organic transformations in the solid state, in particular summarizing the classic works of Ubbelohde and Mnyukh. 23 The weaker interactions in molecular materials can also lead to more extreme behavior under changes in temperature than in conventional materials. This is exemplified by so-called negative thermal expansion (NTE) materials, which show the unusual property of contracting in volume on heating. 24 Most of the "classic" phonon-driven oxide NTE systems such as ZrW 2 O 8 , 25 Sc 2 (WO 4 ) 3 , 26 and zeolites 27 have negative linear contraction coefficients that are of comparable magnitude to the positive coefficients of normal materials (α l ≈ −20−0 × 10 −6 K −1 ). ZrW 2 O 8 , for example, has α l = −9 × 10 −6 K −1 from 2 to 300 K corresponding to a percentage contraction Δl/l ≈ −0.1% over a 100 K range. 28 The term "colossal negative thermal expansion" was introduced to define materials with α l more negative than −100 × 10 −6 K −1 and hence a Δl/l contraction larger than 1% over 100 K. The first such material was Ag 3 [Co(CN) 6 ], which showed a uniaxial NTE of −130 × 10 −6 K −1 ; this extreme contraction is related to the inherent flexibility of its framework structure, in which the volume is defined by a weak Ag−Ag argentophilic interaction. 29 In essence, this soft interaction leads to a large positive expansion in two dimensions, with the framework topology driving a contraction along the perpendicular direction. Colossal isotropic NTE was subsequently reported in other framework systems such as the UiO-66 MOF. 30 Mullaney et al. have also shown how spin crossover can switch the geometry of flexible frameworks; by spin dilution, they could prepare materials with continuous cell parameter changes of +6/−4% over a 60 K range. This is strongly reminiscent of the major "breathing" changes in the geometry of metal organic frameworks such as MIL-5 on gas uptake. 31 Extreme thermal expansion or contraction coefficients are also found in purely organic crystals where weaker intermolecular forces dominate. Some of the most dramatic are in the thermosalient 3,32 or "jumping crystals" such as (phenylazophenyl) palladium hexafluoroacetylacetonate 33 with α a = +260.4 × 10 −6 K −1 between 223 and 348 K and N′-2propylidene-4-hydroxybenzohydrazide, 34 with α a/b ≈ +230 × 10 −6 K −1 and α c ≈ −290 × 10 −6 K −1 over the temperature range 298−373 K. (S,S)-octa-3,5-diyne-2,7-diol 35 has been reported as a biaxial NTE material with α a = +450 × 10 −6 K −1 , α b = −130 × 10 −6 K and α c = −250 × 10 −6 K − giving a relatively low overall volume expansion α V = +60 × 10 −6 K −1 (all 240−330 K). Methanol monohydrate, in contrast, has a large volume expansion α V = +500 × 10 −6 K −1 that causes a more modest contraction in one dimension α a = −60 × 10 −6 K −1 (both at 155 K) along with negative linear compressibility. 36 Here, we report the remarkable thermal expansion properties of a chloranilic acid pyrazine (CA-Pyz) co-crystal associated with a newly-discovered phase transition. The molecular structure and views of the three-dimensional packing (which will be discussed in detail later in the text) are shown in Figure 1.
Powder and single-crystal diffraction studies have shown that this material undergoes a phase transition which leads to extreme distortions of its unit cell. Its volume change from 200 to 300 K is one of the largest known for an organic crystal, and it shows extreme anisotropy in the contraction and expansion of its a and b cell parameters. Average linear thermal expansion coefficients approaching ±1000 × 10 −6 K −1 are observed from 200 to 300 K corresponding to 10% length changes, an order of magnitude larger than required by the definition of "colossal".
Our structural studies and the application of rigid-body rotational symmetry modes allow us to understand and describe the molecular origins of this fascinating behavior. We also present a simple model to explain the unusual temperature evolution of cell parameters that can arise in materials showing such extreme thermal expansion.

■ EXPERIMENTAL SECTION
Sample Preparation. Single crystals of CA-Pyz were obtained by slow evaporation of an acetonitrile solution of chloranilic acid (Aldrich, 98%) and pyrazine (Aldrich, 99%) in a 1:1 molar ratio. Chloranilic acid (0.0627 g, 0.3 mmol) and pyrazine (0.0240 g, 0.3 mmol) were dissolved separately in the minimum volume of acetonitrile (typically 6 and 1 mL, respectively) with gentle heating for 30 min. Orange-red rhombusshaped crystals appeared after 2 days. Polycrystalline samples were produced by gentle grinding of crystals.
Single-Crystal Diffraction. Single-crystal X-ray diffraction data were acquired on an Oxford Gemini S Ultra diffractometer equipped with a CCD area detector, using Mo Kα radiation (λ = 0.71073 Å). Data were collected at 300, 275, 250, 230, 200, and 150 K on both cooling and warming. A Cryostream Plus Controller was used to control the experimental temperature. Crystal structures were solved using SIR92 37 within the CRYSTALS 38 software. All nonhydrogen atoms were refined anisotropically against F hkl 2 . All hydrogen atoms were located by difference Fourier maps and refined isotropically without any restraints. Single-crystal neutron diffraction data were collected on the SXD instrument of the ISIS Neutron and Muon Source at the Rutherford Appleton laboratory. The crystal was attached to a goniometer head using adhesive Al foil and placed in a rotating bottom-loading CCR. Data were collected at 295 K, in 10 crystal orientations for 3 h each. Initial data reduction was done using the SXD2001 software within the IDL virtual machine, and refinement of the structural model was carried out in Jana2006. 39 The fractional coordinates and anisotropic atomic displacement factors were refined for all atoms against F hkl 2 . Translation, libration, screw (TLS) tensors were derived from experimental anisotropic displacement parameters in Platon. 40 Powder Diffraction. Synchrotron powder X-ray diffraction data were collected at a beamline I11 at Diamond Light Source in highresolution mode using the 45 Multi-Analysing Crystal detector and a wavelength λ = 0.8257653 Å (calibrated against a silicon standard NIST 640c). The sample was loaded into a 0.7 mm external-diameter quartz capillary to a length of 30 mm. The capillary was sealed and attached to a brass holder, which rotated during the measurements. Variable temperature data were collected every 4 K between 180 and 360 K. Laboratory powder X-ray diffraction data were collected in capillary mode on a Bruker D8 diffractometer equipped with a Lynx-Eye detector and an Oxford Cryosystems Cryostream Plus device, using Mo Kα radiation. The sample was warmed from 150 to 400 K at a rate of 15 K/h. A series of 20 min datasets were recorded over a 2θ range of 1−30°u sing a step size 0.01°. All powder diffraction data were analyzed using the TOPAS Academic software. 41−43 Solid-State NMR and Thermal Analysis. 1 H solid-state NMR was recorded at 205 and 308 K with a 15 kHz spinning rate on a Bruker Advance III HD instrument. Differential scanning calorimetry (DSC) experiments were performed on a PerkinElmer Pyris 1 DSC instrument. The sample (2.831 mg) was heated from 120 to 520 K at rates between 10 and 100 K/min.
Symmetry-Mode Analysis. Symmetry-adapted distortion modes belonging to the irreducible representations of the parent-symmetry group, commonly referred to as "symmetry modes", were employed here to describe global patterns of rigid-body rotations. For brevity, we refer to such patterns simply as "rotational symmetry modes".
Rotational symmetry modes were defined for a dummy pivot atom placed at the center of inversion of each molecule. Command files containing both a rotational symmetry-mode description and a more familiar displacive symmetry-mode description were generated in a format suitable for TOPAS Academic. Rotational symmetry-mode amplitudes were refined directly using the laboratory powder diffraction data with displacive symmetry modes fixed at zero. Rotational Figure 1. Molecular structure of chloranilic acid (CA) and pyrazine (Pyz), and views of the CA-Pyz co-crystal structure at 300 K along a, b, and c (left to right). The monoclinic high-temperature (HT) unit cell is shown in gray. The bold blue "diamond" in the view of the ab plane shows the low-temperature triclinic cell discussed in the text and used for most analysis. Heavy black and blue arrows show directions of rotational symmetry modes for CA and Pyz, respectively. A chain of hydrogen-bonded CA-Pyz molecules is highlighted in red. symmetry-mode amplitudes were extracted from single-crystal experiments by minimizing the distances between all atoms in a rotational symmetry-mode description with displacive symmetry-mode amplitudes fixed at zero (based on the 300 K single-crystal structure) and the conventionally refined fractional atomic coordinates. The sensitivity of extracted rotational symmetry-mode amplitudes to internal distortions of molecules was assessed by also refining displacive symmetry-mode amplitudes to give a perfect fit to the conventional coordinates but with displacive amplitudes restrained to values as close to zero as possible such that rotational symmetry modes described the majority of the atomic movement. All symmetry-mode calculations were performed using the ISODISTORT software. 44

■ RESULTS AND DISCUSSION
Observation and Analysis of a Structural Phase Transition in CA-Pyz. Figure 2 shows powder diffraction data recorded on warming and subsequent cooling of CA-Pyz from 180 to 360 to 180 K (equivalent lab data used in Figure 4b are given in the Supporting Information (SI) Figure S1). It is immediately apparent from these data that CA-Pyz undergoes a phase transition at around 300 K, and the extreme splitting of certain hkl reflections suggests that the transition is associated with significant changes in the unit cell parameters. We see no   significant features in the DSC at this temperature, but this is perhaps unsurprising given the wide temperature range over which the transition occurs. The 150 K data can be indexed with a triclinic unit cell with a = 4.78 Å, b = 5.83 Å, c = 10.71 Å, α = 82.0°, β = 81.5°, γ = 77.0°, V = 286 Å 3 . Figure 1 shows the relationship of this triclinic cell (bold blue lines) to the previously reported monoclinic hightemperature cell (gray lines). Figure 3 shows unit cell parameters extracted by Pawley fitting, 45 using both the warming and cooling datasets. On warming, we see some peak broadening just below the phase transition temperature T C (300 K), which was modeled using just 4 of the 15 allowed terms of a 4th-order spherical harmonic to describe anisotropic microstrain. 41,46 The magnitudes of the coefficients obtained are included in the SI ( Figure S2).

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At high temperature, the Bragg peaks are essentially as sharp as at low temperature. On cooling, the phase transition is fully reversible, though there is a subtle thermal history-dependent splitting of some of the "tuning-fork" reflections just below the phase transition temperature. By tuning fork, we mean reflections such as the ∼9.5°2θ peak ((11−1) at high T; (011) and (101) at low T), which undergo particularly marked splitting, resulting in the reflections that are equivalent at high temperature being separated by several degrees in 2θ at low temperature. The cooling data can be Pawley-fitted by using three closely related phases just below T C , and we show their unit cell parameters as open points and crosses in Figure 3. Importantly, the sample regains sharp, essentially unstrained peaks at low temperature where the powder diffraction pattern can again be described using a single phase. This is demonstrated, for example, by the convergence of cell parameters of the three Pawley-fit phases to identical values at low temperature. Similar effects have been reported in other high-anisotropy systems such as MIL53 47,48 and could be caused by intergrain effects or the significant microstrain build-up between ∼220 and 300 K, which is shown in the SI ( Figure S2).
Structure of the New (LT) Form of CA-Pyz. To gain detailed insight into the structural changes associated with the phase transition, single-crystal X-ray diffraction experiments were performed at 6 temperatures between 300 and 150 K (on both warming and cooling). The crystallographic parameters are summarized in Tables S1 and S2 and cell parameters plotted in Figure S3. At 300 K, CA-Pyz was found to adopt the previously reported monoclinic structure 49 in space group C2/m with unit cell parameters of a = 8.296(5) Å, b = 6.654(2) Å, c = 10.993(2) Å, β = 101.60(3)°and V = 594.44(11) Å 3 . We refer to this as the high-temperature (HT) form of CA-Pyz. Below this temperature, a new triclinic form (LT form, space group P1̅ ) was observed and its structure was solved from the 150 K data set. The molecular packing in the two forms is very similar, facilitated by a one-dimensional network of O−H···N hydrogen bonding (see Figure 5), which gives rise to the CA-Pyz chains highlighted in red in Figure 1. With the donor−acceptor distance of d ON ≈ 2.7 Å, these are medium-length O−H···N hydrogen bonds. 50 Using the C−O bond lengths (determined from X-ray diffraction more reliably than those involving hydrogen atoms) as a proxy for detecting potential temperature-induced proton migration, we find no evidence of this type of dynamics; these bond lengths remain at about 1.31 Å between 150 and 300 K ( Figure S4), suggesting that the single bond character is retained throughout this temperature region. 51 Similarly, we see no evidence to suggest significant distortions of individual molecules.
Single-crystal neutron diffraction data recorded at 295 K allowed accurate determination of the hydrogen atom positions and anisotropic atomic displacement parameters (ADPs). A view of the ADPs at all temperatures is shown in Figure S5 and for the 295 K structure in Figure 5. The most striking structural feature is the magnitude and the orientation of the ADPs on the atoms in the pyrazine molecule. Ishida and Kashino 49 noted large anisotropic displacements of the C4 atom perpendicular to the pyrazine ring, but their attempts to model these by disordering the carbon atoms around a pseudo two-fold rotation axis passing through the N atoms (i.e., as static disorder) were not successful. This, together with our observation of large Hatom ADPs, suggests a very prominent librational motion perpendicular to the pyrazine ring at a high temperature. As an approximation, a translation, libration, screw (TLS) analysis of the experimental neutron ADPs 52 gives eigenvalues of the librational tensor of the Pyz molecule of ∼22, 8, and 6°and translations of 0.36, 0.23, and 0.1 Å 2 .
Further evidence for the dynamics in the HT form of CA-Pyz comes from 1 H solid-state NMR data recorded at 205 and 308 K ( Figure S6). Both OH and Pyz proton signals undergo significant narrowing on warming: from 950/1490 to 550/600 Hz, respectively. The CA OH chemical shift changes by ∼0.5 ppm indicating a minor change in the proton environment and hydrogen bond network between the two phases.
Rotational Symmetry-Mode Description of the Phase Transition in CA-Pyz. The power of using symmetry-adapted distortion modes belonging to the irreducible representations of the parent-symmetry group (a.k.a. symmetry modes) to describe the order parameters that arise in symmetry-reducing phase transitions is now widely appreciated. 44,53−56 Key advantages are that the essence of the phase transition can often be captured by a small number of parameters (mode amplitudes), each of which quantifies a structural distortion that breaks the parent symmetry in a unique way, and each of which is defined to be zero in the high symmetry parent phase. Symmetry-mode parameters, thus, tend to have clear physical interpretations and origins.
The full parameterization of an arbitrary crystal−crystal phase transition in terms of symmetry modes was initially accomplished for atomic displacements, which are polar vectors. 55−57 The group theoretical calculations required for the construction of displacive symmetry modes are available within the ISODISTORT software package. 44 ISODISTORT also includes symmetry modes to describe the ordering of atomic species (occupational order−disorder), magnetic moments (timereversible axial vectors), and, most recently, rotational moments (non-time-reversed axial vectors). A rotational symmetry-mode approach can give a very compact description of an entire pattern of rotation vectors, where each vector rotates a group of atoms, such as a rigid molecule or polyhedral unit. Note that the three components of a molecular rotation vector capture the same information as would be specified by three rotational angles (e.g., around three orthogonal axes) in a conventional rigid-body description. The rotation vector is more convenient, because it can be directly visualized (see below) and because there are no arbitrary conventions to consider regarding the order of the rotations around different axes. A rotation vector's orientation defines the rotation axis, and its length defines the angle of rotation. 58 These ideas have previously been applied to describe the lowsymmetry structure of the extended solid RbBr 3 Mg(H 2 O) 6 , 59 and, more recently, the unusual high-to-low-symmetry phase transition (on warming) of the molecular ferroelectric 5,6dichloro-2-methylbenzimidazole 60 and the cooperative motions of networks of interconnected rigid units. 61 The refined structures from single-crystal diffraction experiments allow us to develop a straightforward description of the child LT phase of CA-Pyz in terms of the rotational symmetry modes belonging to the Γ 2 + irrep of the parent HT phase. The Γ 2 + irrep of space group C2/m results in a P1̅ subgroup of index 2 with basis {(1/2, 1/2, 0), (1/2, −1/2, 0), (0, 0, −1)} 62 and origin at (0,0,0) relative to the conventional parent cell (the blue cell of Figure 1). The child has 36 displacive symmetry modes (spanning the same space as the 36 free xyz atom-position parameters in the conventional description), 24 of which (the Γ 1 + modes) describe structural degrees of freedom already present in the parent. Alternatively, if we assume rigid molecules, which merely rotate around their respective inversion centers, we need only consider 6 rotational symmetry modes (spanning the same space as the 6 free xyz components of the two molecular rotation vectors). The LT phase has a Γ 1 + and two Γ 2 + irrep modes for each molecule, which are illustrated in Figure 1 For small rotations of rigid molecules, these 6 parameters should allow us to capture the key features of the phase transition. If additional molecular distortions occur, these can be described by refining additional displacive symmetry-mode amplitudes as internal degrees of freedom within the "semirigid" bodies. These internal modes can also be used to correct for distortions caused by large changes in cell metric when rigid bodies are defined using parent fractional coordinates. If one attempts to simultaneously use both 6 rotational symmetry modes and 36 displacive symmetry modes to describe the structure, then the description will, of course, be overparameterized. This is corrected by removing 6 appropriate linear combinations of displacive symmetry modes that result in pure rotations. Alternatively, one can use soft restraints to keep unnecessary displacive symmetry-mode amplitudes close to zero during refinement, forcing the rotational symmetry modes to "do most of the work" in describing atomic coordinate shifts. We adopt this latter approach for part of our analysis.

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Rotational symmetry-mode amplitudes, extracted by fitting the rotating rigid bodies (as defined using the 300 K high symmetry parent structure) to the refined conventional atomic coordinates from lower temperature single-crystal datasets, are shown in Figure 4a. Figure 4b shows equivalent mode amplitudes refined directly from relatively low-quality laboratory powder diffraction data. The good qualitative and quantitative agreement between Figure 4a and 4b shows that this restricted parameter set (in contrast to traditional xyz refinements) can be reliably extracted from low-quality  laboratory powder diffraction data. We see from these plots that Γ 2 + rotations (circles) have by far the highest magnitude and are, therefore, the most important in describing and understanding the phase transition. Pyz molecular rotations (open markers) are also much more important than those of the CA molecule (closed markers). Figure 4d displays the resulting rotation vectors for each molecule. For Pyz, we see that the large ∼16°r otation is almost aligned with the N−N vector. For CA, the smaller ∼4°rotation is approximately perpendicular to the CO vector and slightly out of the molecular plane. We emphasize that the mode amplitudes of Figure 4a, or their simpler representation in Figure 4g, describe the structural changes that occur due to the phase transition. From the temperature dependence of r 4 , we see that the effects of the transition are apparent from ∼150 to 300 K.

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As with any rigid-body description, there are approximations in this approach such that the rigid-body coordinates will be slightly different to those from free refinement. Some differences arise from the fact that at high temperatures, the relatively rigid molecules undergo correlated vibrational motions leading to the well-known underestimation of bond lengths when using harmonic displacement parameters. 63 The magnitude of this effect can be appreciated from the left-hand panels of Figure 5, which show anisotropic displacement parameters extracted from neutron single-crystal diffraction refinements. These lead to the HT Pyz molecule showing shorter apparent bond lengths than at low temperature. Our TLS analysis of the neutron-derived structure gives observed and corrected C−N distances of 1.275 and 1.360 Å, respectively. These compare to bond lengths of 1.269 and 1.346 Å obtained from single-crystal X-ray data at 300 K and 150 K, respectively, confirming the librational shortening. Distortions due to the extreme changes in cell metric observed in this particular compound also lead to atoms being up to 0.1 Å from true positions in the molecular rotation description. If internal displacive symmetry-mode amplitudes are refined to give perfect atomic overlap with a restraint applied so that as much of the atomic displacements are captured by rotational symmetry modes as possible, the values of r 1 to r 6 (as shown in Figure 4a) change very little. The rotating rigid-body model, therefore, captures most of the key structural changes in a small number of parameters that can be routinely and reliably determined.
Remarkable Thermal Expansion Behavior of CA-Pyz. We can adopt a similar language to describe the cell parameter changes relative to 300 K that occur on cooling. This involves using strain modes, which transform as polar symmetrized second-rank tensors. The six degrees of freedom of the lowtemperature cell appear as four parent-allowed Γ 1 + strain modes (labeled here s 1 −s 4 ) and two parent-symmetry-breaking Γ 2 + modes (s 5 and s 6 ); their amplitudes are shown in Figure 4c. As expected, Γ 2 + strains refine to essentially zero above T c = 300 K for the monoclinic HT phase but show a marked deviation from 0 below 300 K, with the Γ 2 + s 5 strain reaching a remarkable −0.14 (−14%) by 180 K. It also seems that the Γ 1 + strains show a different temperature dependence than those of Γ 2 + irrep, with significant deviations from their high-temperature extrapolated behavior only appearing below T ≈ 260 K. The Γ 2 + s 5 mode also displays a clear discontinuity at this lower temperature.
The influence of the strain modes on individual cell parameters depends on the cell setting used. To properly decouple the physical changes of the crystal from the cell setting, we have calculated thermal expansion along the principal axes of the expansion tensor. Figure 4e−g shows expansion indicatrices considering just Γ 1 + , just Γ 2 + , and Γ 1 + + Γ 2 + overall strains and their relationships to the parent cell axes. As anticipated from Figure  2, we see extremely large negative thermal expansion (blue) close to the parent b-axis, extremely large positive expansion (red) close to the a-axis, and more normal (though still large) positive expansion close to the c-axis. Average thermal expansion coefficients over a 200−300 and 250−300 K temperature range are given in Table 1, and their full temperature evolution is plotted in Figure 3e. We see that the extreme uniaxial contraction (α l = −1500 K −1 at 250 K) is dominated by Γ 2 + strains, and that the dominant effect of Γ 1 + is an expansion of the interlayer c-axis. If we use a nonstandard C1̅ setting for the child structure, we, of course, see the same temperature dependence of strain modes, but they manifest in a different temperature dependence of cell parameters (see SI Figure S7 and discussion  below). In this alternative description, the large −14% amplitude of the s 5 Γ 2 + mode predominantly influences the cell angle γ, which changes from 90 to ∼101.5°between 300 and 150 K.

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The trigonometric dependencies of the individual child-cell parameters on the strain modes are considerably more complicated than that of the volume. However, we can expand these dependencies to first order and then apply the observed 150 K strain-mode amplitudes to determine which contributions are most important to the thermal expansion (Table 2). These approximations also help to rationalize the extremely unusual temperature dependencies of the cell parameters in Figure 3. For example, the unit cell angle β initially decreases on cooling through T c but then increases below T ≈ 260 K, whereas angle increases monotonically on cooling. When we look at which modes influence α and β, we see that they vary in opposite directions with respect to either mode s 5 or s 6 of Γ 2 + ; the sensitivity to s 5 is weak and the amplitude of s 5 is large, whereas the sensitivity to s 6 is strong and the amplitude of s 6 is small. As a result, s 5 and s 6 end up making comparable angle changes of magnitudes 0.811 and 0.575°at 150 K. The total contributions of Γ 2 + are then Δα = 0.811 − 0.575 = 0.236°and Δβ = −0.811 + 0.575 = −0.236°. The sizeable amplitudes of modes s 2 and s 4 of Γ 1 + must also be considered, especially due to the high sensitivity of both angles to s 2 ; the total contributions of Γ 1 + strains are Δα = Δβ = 1.019 −0.199 = 0.820°at 150 K, which are ultimately much larger than those of Γ 2 + . The combined multiirrep contributions (Γ 1 + + Γ 2 + ) are then Δα = 0.820 + 0.236 = 1.056°and Δβ = 0.820 − 0.236 = 0.584°at 150 K. However, because the Γ 1 + modes acquire significant amplitudes only well below the 300 K transition (Figure 4c), the Γ 2 + decrease in Δβ with decreasing temperature is well underway, before the much larger Γ 1 + increase in Δβ begins to evolve, resulting in the striking trend reversal observed.
Although less obvious from Figure 3d, similar effects are seen in the cell volume, which shows a marked discontinuity at 260 K and a smaller discontinuity at 300 K. This is more apparent in the plot of volumetric strain relative to that extrapolated from the HT structure in Figure 3f and the thermal expansion plots of (1/a)da/dT in Figure 3e. Unlike the individual cell parameters, the dependence of the cell volume on the strain amplitudes is relatively simple (a third-order multivariable polynomial) Δ = + + + + + ), we see that the volume change is approximately linear in, and hence very sensitive to, strains s 1 , s 3 , s 4 , which tend to operate primarily on the cell-edge lengths. In contrast, the volume change is merely quadratic in, and hence much less sensitive to, strains s 2 , s 5 , s 6 , which tend to operate primarily on the cell angles. As a result, despite the fact that the Γ 2 + strain s 5 dominates the structural (and presumably the energetic) changes, the much smaller Γ 1 + strain s 4 makes the dominant contribution to the volume change.
It remains to explore why the primary Γ 2 + strain modes and secondary Γ 1 + strain modes evolve at such different temperatures. In this context, the word "secondary" implies the mathematical inability to generate the low-symmetry subgroup and hence the physical inability to drive the transition; in this case, the secondary modes do not break any parent symmetries at all since Γ 1 + is also the identity irrep. One possible explanation is the occurrence of a second-phase transition near 260 K, which would necessarily be isosymmetric (space group P1̅ is retained) and first order since its order parameter belongs to the identity irrep. We see no strong evidence to support such a phase transition in our data. In addition, a closer examination of Figure  4c reveals that the secondary Γ 1 + modes exhibit small but nonzero departures from their high-temperature trends between 260 and 300 K. We, therefore, believe that the observed behavior is caused by a coupling between the primary Γ 2 + and secondary Γ 1 + order parameters. In essence, for strains as large as those observed in CA-Pyz, cross-coupling terms in the Landau freeenergy expansion become sufficiently large that they can no Right-hand columns show each principal-axis direction relative to crystallographic axes for the overall strain (i.e., components of Xn directions along a, b, and c, as shown in Figure 4g). Estimated uncertainties on expansion coefficients are ∼30 × 10 −6 K −1 .  The values in a given column can be summed to determine the approximate total change in the corresponding cell parameter. Some of the smaller nonzero 150 K values were rounded to zero. For example, the pseudo-linear slope of the Δc(s 2 ) curve is −3.061 Å, so that a value of s 2 = +0.0169 (at 150 K) results in a change of Δc ≈ (−3.061 Å)(0.0169) = −0.052 Å, in addition to Δα = Δβ ≈ (+1.050)(0.0169)(180°/π) = +1.019°.  Figure 5. Rotational symmetry-mode refinement shows that the main structural change is a cooperative rotation of all Pyz molecules in the z = 0 plane, which occurs around an axis close to the H···N(Pyz)N···H hydrogen bond direction (animations available in the SI). This is dominated by the r 4 Γ 2 + rotation, with the smaller r 5 Γ 2 + contribution acting to bring the rotation vector in line with the H-bonded chain. The significant shift in Pyz positions driven by the rotation couples with a sliding of adjacent planes of CA molecules, with each layer moving laterally from its high-temperature position by ∼1 Å between 300 and 250 K. This is enabled by the relatively weak van der Waals interactions between CA planes and leads to the significant expansion of the b-axis on cooling. In addition to the dominant Γ 2 + rotations, we see a small r 6 Γ 1 + rotation below 260 K (shown with squares in Figure 4a). This corresponds (Figures 1 and 5) to a rotation of Pyz around an axis perpendicular to the N−N direction and in the plane of the ring. This motion "buckles" the CA-Pyz chain, causing a reduction in the c axis (∼0.2 Å) and a small expansion on cooling in the ab plane (∼0.1 Å increase in γ ab sin( ) as an in-plane measure of the dimension) as the Pyz plane becomes more closely aligned with it. It seems likely that this distortion occurs as a result of the large r 4 rotation and provides the observed coupling between Γ 2 + and Γ 1 + strains that emerges with the decreasing temperature.

■ CONCLUSIONS
Our variable temperature single-crystal and powder diffraction studies have shown that CA-Pyz undergoes a reversible phase transition close to room temperature, which leads to extreme anisotropy in thermal expansion and a remarkable 14% size reduction in one dimension over a 100 K range. The effects of the transition are seen over a ∼150 to 300 K temperature range. Highly anisotropic thermal expansion coefficients up to +1500 and −1500 × 10 −6 K −1 result. These occur over a significant temperature range close to room temperature and without any external driving effects such as spin crossover or composition change. In the HT form, anisotropic atomic displacement parameters derived from neutron diffraction data suggest significant (∼22°) librational disorder of pyrazine molecules around an axis defined by the H···N(Pyz)N···H hydrogen bonds, which freeze out as a ∼16°static rotation on cooling. The transition, which is presumably entropically driven, is enabled by the cooperative sliding of adjacent molecular layers by ∼1 Å and leads to the high thermal anisotropy. It, thus, has similarities to the alkyl-chain disorder reported in a Co complex, 64 which leads to cell parameter changes of +8/−5% at a first-order transition, and to the abrupt uniaxial contraction caused by oxalate reorientation in [Ni II (en) 3 ](ox). 65 It differs from these examples in that the transition is second-order-like and occurs over a broad temperature range. The cooperative nature of the structural change, which involves relatively small displacements of adjacent layers, and the relationship between the parent and child cells is reminiscent of a diffusionless martensitic transition. It is, therefore, likely that a similar change can be stress-induced, potentially leading to phenomena such as superelasticity or shape memory. Extreme cell parameter changes are often associated with martensitic transitions. For example, the transitions in NiTi and the organic superelastic terephthalamide 13 correspond to respective cell parameter changes approaching ±10 and ±7%.
This work also shows that rotational symmetry modes provide a powerful symmetry-derived description of the phase transition in CA-Pyz, allowing us to describe the essence of the structural changes in a small number of parameters, principally a Γ 2 + strain and rotation. The use of strain modes to describe thermal expansion also allows us to understand the unusual temperature dependence of cell parameters in this material in terms of coupling between primary and secondary order parameters. These methods can be used for a wide range of molecular and hybrid materials undergoing phase transitions and can be readily applied using the ISODISTORT and TOPAS approaches, allowing useful information to be determined on such materials even using relatively low-quality powder diffraction data.