Flexibility transition and guest-driven reconstruction in a ferroelastic metal–organic framework

The metal–organic framework copper(i) tricyanomethanide, Cu(tcm), undergoes a ferroelastic transition on cooling below Tf = 240 K. Thermal expansion measurements reveal an order-of-magnitude variation in framework flexibility across Tf. The low-temperature phase α-Cu(tcm) exhibits colossal positive and negative thermal expansion that is the strongest ever reported for a framework material. On exposure to acetonitrile, Cu(tcm) undergoes a reconstructive solid-phase transition to acetonitrilocopper(i) tricyanomethanide. This transition can be reversed by heating under vacuum. Infrared spectroscopy measurements are sensitive to the phase change, suggesting that Cu(tcm) may find application in solid-phase acetonitrile sensing.


Introduction
Framework materials with the wine-rack topology have emerged as an important class of materials because their characteristic low-energy 'breathing' mode allows for extreme mechanical responses to external stimuli. [1][2][3] Examples include sorption-and temperature-driven breathing in the so-called MIL family of metal-organic frameworks (MOFs), 4,5 and colossal positive/negative thermal expansion (PTE/NTE) and negative linear compressibility (NLC) in the transition-metal dicyanometallates. [6][7][8] In all cases framework breathing couples expansion in one direction to contraction in a perpendicular direction, with the framework angle θ approaching 90°f or increased framework volumes [ Fig. 1]. While it is usually symmetry-allowed for these systems to adopt arbitrary geometries (i.e. values of θ), in some cases the θ = 90°limit actually corresponds to a higher space group symmetry. 9 For this square geometry, framework breathing is symmetry forbidden, resulting in a fundamental increase in rigidity. So the existence of a 'flexibility transition' between low-and highsymmetry geometries would allow wine-rack frameworks to be switched between compliant (low-symmetry, θ ≠ 90°) and rigid (high-symmetry, θ = 90°) states.
Such transitions are well established in the field of conventional ceramics, where they are usually discussed in the context of ferroelasticity. [10][11][12][13] The magnitude of symmetrybreaking strain ε [= (b − a)/(a + b) for a tetragonal-orthorhombic transition] acts as an order parameter just as magnetisation does for ferromagnets and polarisation for ferroelectrics. In this way, the rigid high-symmetry 'paraelastic' state of Fig. 1 corresponds to ε = 0 and the flexible low-symmetry 'ferroelastic' state to ε > 0. The crucial difference between MOF-type systems and conventional ceramics is that the extreme mechanical flexibilities of the former allow, in principle, for very much larger strains to develop across a ferroelastic transition. Consequently the flexibilities of paraelastic and ferroelastic states may be substantially more different for these materials than is the case for conventional inorganics. While there are a handful of very recent studies of ferroelastic transitions in MOFs, 14,15 and indeed switching between 'narrow pore' and 'large pore' states of pillared MOFs might be interpretable in terms of an improper ferroelastic response, 9 there remains a clear need to establish a model system in which ferroelasticity drives a fundamental change in framework flexibility.
Here we show that the previously-unreported framework material copperĲI) tricyanomethanide, Cu(tcm), exhibits a ferroelastic transition at a critical temperature T f = 240 K. Under ambient conditions, this system adopts a tetragonal wine-rack topology, for which breathing is symmetry forbidden. On cooling below 240 K the crystal symmetry lowers to an orthorhombic subgroup, for which breathing is symmetry allowed. Measurement of the coefficients of thermal expansion α allows quantification of the flexibility of both high-and lowtemperature phases; we find that values of α within the ferroelastic phase are more than an order of magnitude larger than within the paraelastic phase. In fact the NTE effect we observe, α = −407(28) MK −1 (20 < T < 240 K), is many times larger than the most extreme sustained NTE behaviour ever reported: α ≃ −170 MK −1 for FMOF-1, 16 6 ], 6 and α = −80(12) MK −1 for the pillared zinc/ terephthalate MOF of ref. 9. Consequently, T f signifies not only the emergence of symmetry-breaking strain, but also a fundamental shift in the degree of framework flexibility.
In an attempt to explore the extent to which a similar transition might be brought about by guest uptake, we find that Cu(tcm) is reversibly convertible into a topologically-distinct solvate ĳCuĲMeCN)Ĳtcm)] upon exposure to acetonitrile. Involving reconstruction between triply-interpenetrating (10,3)-b and interdigitated (6,3) nets, this solid-solid transformation highlights the extreme coordinative lability of Cu + ions in the parent system. The two frameworks are distinguished not only by their network topology but also by their spectroscopic behaviour, suggesting that Cu(tcm) might find application as a solid-phase acetonitrile sensor.

Methods
All reagents were obtained from commercial suppliers and used as received.

CopperĲI) tricyanomethanide
Synthesis of copperĲI) tricyanomethanide followed the reduction protocol reported elsewhere for the related binuclear compound bis-(tricyanomethanido)-tetrakis-(triphenylphosphine) dicopper(I). 17 A saturated aqueous solution of copper(II) sulfate (Sigma Aldrich, 99%; 0.3991 g) was reduced by dropwise addition of a concentrated aqueous solution of excess sodium hydrogen sulfite (Sigma Aldrich, 0.3587 g). The resulting mintgreen solution was stirred for 30 min, after which time an aqueous solution of a stoichiometric quantity of potassium tricyanomethanide (Alfa Aesar; 0.3229 g) was added dropwise. A fine, off-white precipitate formed immediately. After further stirring for 2 h, the precipitate was filtered, washed with H 2 O, and dried under vacuum to afford a polycrystalline sample of copper(I) tricyanomethanide.
CopperĲI) tricyanomethanide could also be obtained by heating the acetonitrile complex (see below) under vacuum at 473 K for 12 h.

AcetonitrilocopperĲI) tricyanomethanide
Polycrystalline samples of acetontrilocopperĲI) tricyanomethanide were prepared by mixing acetonitrile solutions containing stoichiometric quantities of tetrakis(acetonitrilo)copper(I) triflate (Sigma Aldrich, 0.9421 g) and potassium tricyanomethanide (Alfa Aesar, 0.3229 g). The reaction mixture was stirred for 2 h and the off-white precipitate filtered and then dried under vacuum to afford acetonitrilocopper(I) tricyanomethanide in quantitative yield.
Single crystal samples of acetonitrilocopperĲI) tricyanomethanide could be obtained using slow-diffusion techniques. To separate arms of a glass H-tube were placed chilled acetonitrile solutions of potassium tricyanomethanide (Alfa Aesar, 47.18 mg) and tetrakis(acetonitrilo)copper(I) tetrafluoroborate (Sigma Aldrich, 320.0 mg). Further chilled acetonitrile was then carefully added until the cross-bar was filled. After a period of 14 d, small colourless single crystals suitable for single-crystal X-ray diffraction measurements had formed.
AcetonitrilocopperĲI) tricyanomethanide could also be made by exposing dry copper(I) tricyanomethanide to a few drops of acetonitrile and leaving for 12 h, then filtering and drying at 50°C under vacuum.

Single-crystal X-ray diffraction
Single-crystal X-ray diffraction data were collected for acetonitrilocopperĲI) tricyanomethanide using an Agilent Technologies SuperNova diffractometer (Cu Kα radiation, λ = 1.5418 Å) at 100 K using an Oxford Cryosystems cryostream, 18 scanning about the ω and ϕ circles. The data were integrated and corrected for absorption using CrysAlisPro, the structure was solved in Pbca using SIR92 (ref 19) and refined using CRYSTALS. 20 All non-hydrogen atoms were refined anisotropically; hydrogen atom positions were refined against the low angle data, according to the procedure described in ref. 21, and were then constrained to ride on their host atoms. A final R-factor of 1.99% was obtained. Crystal structure refinement details are given in Table 1.

Powder X-ray diffraction
All samples were assessed for crystallinity and purity via their X-ray powder diffraction patterns, measured using a Philips PW1730 diffractometer (Cu Kα radiation, λ = 1.541 Å) over the angular (2θ) range 10-70°using a step size of 0.05°. Higherquality diffraction patterns were collected using a PANalytical X'Pert PRO diffractometer (monochromated Cu Kα 1 radiation, λ = 1.54060 Å) using the same angular range and a step size of 0.008°.
Variable-temperature powder X-ray diffraction patterns were measured on a Siemens D5000 X-ray diffractometer (Cu Kα radiation, λ = 1.5418 Å) fitted with an Oxford Cryosystems PheniX cryostat. For temperatures below 300 K the copperĲI) tricyanomethanide sample was combined with vaseline and then loaded into the sample holder. Data collections were carried out every 10 K on heating from 20 to 290 K. Scans were~5 h long and were carried out over the angular range 5°< 2θ < 120°using a step size of 0.02°. Four minute intervals between data collections allowed for temperature equilibration of the sample.
All fits to X-ray powder diffraction data were carried out using TOPAS Academic; 22 in general a modified Thompson-Cox-Hastings pseudo-Voigt (TCHZ) peak shape with a simple axial divergence correction was used and the large anisotropic strain found in this system was accounted for by using a Stephens anisotropic peak broadening term. 23 Rietveld refinement of the room and low-temperature (20 K) structures of αand β-CuĲtcm) were carried out. For the room temperature structure all atom positions were refined with appropriate bond distance (Cu-N, C-N and C-C) and bond angle restraints; the Cu isotropic atomic displacement parameter was refined freely and all atoms within the tcm moiety were constrained to have equal isotropic displacement parameters. A fourth-order spherical harmonic correction was used to account for preferred orientation. At low temperature, the tcm group was refined as a rigid body and all thermal parameters were fixed. Sample environment peaks were identified by their persistence across the α-β transition and were fitted using the Pawley method. Variable-temperature lattice parameters were determined by using sequential (seed-batch) Pawley fits to data in Fdd2 and I4 1 md, where the starting lattice parameters for each temperature were those found for the previous temperature.

Thermogravimetric analysis
Thermogravimetric measurements were carried out using a Perkin Elmer TGA 7, with Perkin Elmer TAC 7/DX thermal analysis controller, from 30 to 600°C at a rate of 10°C min −1 under flowing nitrogen.

Infrared spectroscopy
Infrared spectra were measured using a Bruker Tensor 27 FT-IR spectrometer fitted with an attenuated total reflectance diamond. A small amount of powdered sample was pressed onto the diamond surface and spectra were measured over the range 4000-600 cm −1 . Background scans were recorded before each measurement. Absolute transmittance values were normalised to the tricyanomethanide C-N stretch (2200 cm −1 ) for each measurement.

Results and discussion
CopperĲI) tricyanomethanide structure Having prepared a sample of Cu(tcm), its crystal structure was determined using powder X-ray diffraction methods. The ambient-temperature powder X-ray diffraction patternshown in Fig. 2(a)-could be indexed according to a tetragonal cell with lattice parameters a = 7.539Ĳ2) Å and c = 9.034(3) Å. A Pawley fit confirmed the space group assignment I4 1 md. Based on the cell metric and space group symmetry, a structural model was proposed in which both Cu atoms and tcm groups were centred on the 4a Wyckoff positions, with z = 0  for the former and z ≃ 1 2 for the latter. Using this initial model as a starting point, Rietveld refinement gave a satisfactory fit to data [ Fig. 2(a)]. The corresponding atomic coordinates and atomic displacement parameters are given in Table 2, and the crystal structure is illustrated in Fig. 3(a-c). In this structure, both Cu + and tcm − ions are three-coordinate and connect to form a three-dimensional network with the (10,3)-b topology (Schläfli symbol 10 3 ). This network is sufficiently open that three such nets interpenetrate to give a structure related to that of the MOF Δ-[Cr(Hbiim)(H 2 biim 2 )]SO 4 ·H 2 O (biim = biimidazole). 24,25 The established structural chemistry of copperĲI) tricyanomethanides is limited to ternary and quaternary systems of the form [Cu(tcm)(N-donor)]·{guest}. 26 This is perhaps surprising, given that the analogous silver(I) complex Ag(tcm) has been known for some time. 27 The stronger preference for tetrahedral coordination over trigonal coordination for Cu + relative to Ag + may be an important factor at play in determining the different accessibilities of these two phases. It now seems that both Cu(tcm) and Ag(tcm) adopt polar crystal structures based on three-coordinate M(I)/tcm geometries, but in contrast to the three-dimensional topology of Cu(tcm) the structure of Ag(tcm) is described by stacked, pairwiseinterwoven (6,3)-net layers. 27,28 Despite our reliance here on powder diffraction methods for structure solution and refinement, the relatively small number of structural parameters and the good quality of fit-to-data give us confidence in the structural model we have determined for Cu(tcm). There is no risk of confusion with the Ag(tcm) structure, which would predict a very different powder diffraction pattern to that observed in our measurements. For completeness, we note that the Cu-N bond lengths and N-Cu-N bond angles we obtain (d

Variable-temperature behaviour
Powder X-ray diffraction patterns collected over the temperature range 20 < T < 290 K reveal a second-order phase transition near T f = 240 K that involves splitting of a number of diffraction peaks in a manner consistent with a reduction from tetragonal to orthorhombic symmetry [ Fig. 4(a)]. There are two maximal subgroups of I4 1 md with orthorhombic symmetry: namely, Fdd2 and Imm2. The reflection conditions differ between these two cases, and we found that our data were consistent only with the former. Making use of the appropriate cell transform   The inset shows the chemical structure of the tricyanomethanide anion. (c) The same framework, viewed slightly away from c, illustrating its square wine-rack geometry with θ = 90°. (d) The low-temperature α-Cu(tcm) phase-shown here in terms of the structural model determined using powder X-ray diffraction data collected at 20 K-has the same network connectivity, but the loss of tetragonal symmetry allows θ to deviate from 90°. The Fdd2 unit cell, shown here in black, has twice the volume of the I4 1 md cell of β-Cu(tcm).
we obtained an approximate structural model for the lowtemperature phase, from which Rietveld refinement was possible. The Rietveld fit obtained using data collected at 20 K is shown in Fig. 2(b). The quality of fit is satisfactory, though we note that severe anisotropic peak broadening associated with large lattice strains and also the experimental constraints of measuring diffraction data at 20 K have both degraded the fit relative to that achieved for data collected under ambient conditions. Because of the presence of anisotropic peak broadening, we have not explored the possibility of further symmetry lowering beyond Fdd2; nevertheless, any additional symmetrylowering distortions-if present-must be very much weaker than the orthorhombic strain itself, which dominates the phase transition behaviour at T f . Moreover, because the lowangle peak intensities are well accounted for by the Rietveld model, we can be confident that the transition is displacive (i.e., the framework connectivity is maintained). The transition from I4 1 md to Fdd2 is a ferroelastic transition associated with softening of the Γ 3 zone-centre mode. 29 The corresponding spontaneous strain is expected on the basis of Landau theory to vary as    T T f 1 2 near T f (i.e., the transition should be second order). Experimental values of ε determined from our lattice parameter data are shown in Fig. 4(d) and are consistent with this expected temperature dependence, indicating that this is a proper (i.e. strain-driven) ferroelastic transition. 13,30 A combination of spectroscopic measurements and lattice dynamical modelling would help determine the microscopic driving force for Γ 3 mode softening. Here we note only that this mode allows tilting of the tcm units about an axis parallel to c, which has the effect of reducing slightly the distance between tcm groups of one framework and Cu + centres of the other two interpenetrated frameworks. Consequently, at low temperatures there may be a small electrostatic driving force for symmetry lowering that is overcome by the increased vibrational entropy of the I4 1 md geometry only for temperatures above T f . The atomic coordinates and atomic displacement parameters determined from our Rietveld refinement for the lowtemperature phase are given in Table 3, and the crystal structure itself is illustrated in Fig. 3(d). From this structural model it is clear that the framework connectivity is entirely preserved across T f . The single most important difference between high-and low-temperature phases of Cu(tcm) is the framework angle θ: in the former it is identically equal to 90°w hereas in the latter it is reduced to θ = 2 tan −1 a b 20 K. Noting the parallel to symmetry-breaking transitions in various well-known framework silicates such as cristobalite and quartz, we borrow from the terminology of that field and denote the high-temperature phase as β-CuĲtcm) and the low-temperature phase as α-Cu(tcm). Access to variable-temperature diffraction data allows us to explore the mechanical flexibility of both αand β-CuĲtcm) in terms of their linear coefficients of thermal expansion, and so to determine whether the intuitive picture developed in Fig. 1 does indeed hold in practice. For β-Cu(tcm) there are two independent coefficients of thermal expansion, corresponding to the behaviour parallel and perpendicular to the tetragonal c axis:  Table 3 Structural parameters for α-CuĲtcm) as determined by Rietveld refinement against powder X-ray diffraction data collected at 20 K. Space group: Fdd2. Lattice parameters: a = 9.297(5) Å, b = 11.891(5) Å, c = 9.093(5) Å. All displacement parameters were fixed at B iso = 2 Å 2 Our data give α a = +10.8(23) MK −1 and α c =−21Ĳ4) MK −1 , 31 which-although anomalous in sign and magnitude for conventional framework materials (a ≃ 10 MK −1 )-are comparable to the values obtained for many MOFs. [32][33][34][35][36] In such systems the low energies of transverse vibrational modes tend to favour NTE, which then often drives anomalously large PTE in other crystal directions. 32 Within the lowtemperature α-Cu(tcm) phase, the behaviour along c is essentially unchanged: here we find α c = −13.6(11) MK −1 over the temperature range 20-240 K [ Fig. 4(c)]. In contrast, the behaviour along the a and b axes is fundamentally different from that observed in β-Cu(tcm) because these are the axes affected by changes in the framework angle θ. Linear fits to our data over the same temperature range 20-240 K give α a = +591(28) MK −1 and α b = −407(28) MK −1 . There is clearly a drastic increase in thermal expansivity-and hence framework flexibility-on cooling below T f , justifying our characterisation of the α/β-phase transition as a 'flexibility transition' in Cu(tcm).
The extraordinarily large coefficients of thermal expansion observed here for α-CuĲtcm) deserve further comment because they exceed even the threshold for so-called 'colossal' NTE and PTE (|α| = 100 MK −1 ). 6 Examples of colossal thermal expansion remain extremely rare, even amongst MOFs. Until recently, 'FMOF-1' exhibited the strongest known thermal expansion behaviour: its coefficients of thermal expansion are α a = +230 MK −1 and α c = −170 MK −1 . 16 More extreme PTE has since been observed in the zinc terephthalate-based MOFs of ref. 9 for which α b = +340(35) MK −1 over the temperature range 303-463 K. 31,37 Yet the response we see here for α-Cu(tcm) is larger again by some margin; in particular, the uniaxial NTE along b is so extreme that an aligned composite containing just 2.5% Cu(tcm) would be sufficient to counteract the PTE effect of conventional engineering materials. Moreover, the temperature range over which this NTE occurs (20-240 K)perhaps problematic for some applications-is nonetheless relevant to industries such as aerospace.
But why is α-CuĲtcm) so very flexible? Empirically it is found that framework flexibility tends to scale inversely with metal-ligand interaction strength. 32,38,39 Here, the low charge densities of Cu + and of the terminal N atoms of the tcm − ion 40 will reduce any electrostatic contribution to the thermodynamic cost of framework flexing. Furthermore the combination of a closed-shell d 10 configuration together with low Cu 3d-tcm π * overlap will mean that (directional) covalent effects are also much smaller than in many other MOFs. Consequently, the mechanical properties of this system would be expected to be especially sensitive to low-energy interactions such as dispersion forces, which are well-known to drive extreme thermal expansion in other framework materials. 6 Quantum mechanical calculations would help understand more fully the origin of this extreme mechanical flexibility. 4,5,41

Solvent-induced reorganisation
Exposure of a polycrystalline sample of Cu(tcm) to acetonitrile gave rise to a new phase with a powder diffraction profile quite distinct from that of either αor β-CuĲtcm). TGA measurements of this phase revealed a mass loss of 19% at 400 K, which suggests the formulation [Cu(MeCN)(tcm)] (expected mass loss 21%) [ Fig. 5(a)]. We found that singlecrystal samples could in fact be obtained directly from acetonitrile solution, which allowed us to determine the crystal structure using single-crystal X-ray diffraction methods. Our structure solution is illustrated in Fig. 6(a), confirming the formulation [Cu(MeCN)(tcm)]; key structural parameters are given as ESI. † In this structure, the Cu + ions now have tetrahedral coordination, with one coordination site occupied by a MeCN group; the tcm − ion remains trigonal in its coordination. From a topological perspective, both Cu and tcm components are effectively three-coordinate, connecting to form (6,3) honeycomb layers (Schläfli symbol 6 3 ). These layers stack without interpenetration, in contrast to the related acetonitrile derivative [Ag(MeCN)(tcm)] reported elsewhere [ Fig. 6(b-c)]. 42 Of greatest relevance to this study is the clear difference in connectivity between the structures of Cu(tcm) and ĳCuĲMeCN)Ĳtcm)]. Generation of the latter by exposure of the former to acetonitrile must proceed by concerted cleavage and reconstruction of Cu-tcm bonds, which in itself demonstrates a remarkable coordinative flexibility of the original framework. The closed-shell d 10 electronic configuration of Cu + facilitates bond cleavage, and allows the formation of network structures with coordination numbers between two and four. 43,44 Moreover, this interconversion process is reversible: powder samples of [Cu(MeCN)(tcm)] -themselves prepared by exposing Cu(tcm) to MeCNrevert to β-Cu(tcm) on heating at 200°C for 3 h [Fig. 7]. This series of solid-solid transformations can be followed using infrared spectroscopy, with the acetonitrile-containing phase exhibiting an additional characteristic absorption at 2101 cm −1 associated with the nitrile C-N stretch [ Fig. 5(b)]. Samples of Cu(tcm) exposed to moist air over extended periods show no structural transformation, so the binding of MeCN appears to be strongly selective even in the presence of competitive ligands such as H 2 O. This observation suggests that, like the recently-reported CuCN-based systems of ref. 45, and quite separate from its extreme thermal expansion behaviour, Cu(tcm) may find application in acetonitrile sensing.

Conclusions
In summary, the 'wine-rack'-type framework material Cu(tcm) exhibits a ferroelastic transition at 240 K. This transition demarcates an order-of-magnitude change in elastic response, seen here most obviously in the 'colossal' PTE and NTE effects of α-CuĲtcm) that disappear in β-Cu(tcm). Indeed this anomalous thermal expansion behaviour establishes a new record within the field that means that Cu(tcm) may find application in the athermalisation of functional composites.
With respect to the ferroelastic transition itself, there are strong qualitative parallels to well-known tetragonal/ orthorhombic transitions in oxide frameworks such as As 2 O 5 , 30 for which the elastic anomalies associated with ferroelasticity affect not only the thermal expansion, but also the lattice dynamics (e.g. mode softening, phonon lifetimes), microdomain formation, twin-wall motion, and susceptibility. While our study has been limited to determination of the thermal variation in lattice parameters, we anticipate that further investigation of elastic behaviour in Cu(tcm) at T f may prove informative in establishing parallels between conventional and MOF-type framework materials. 14,46 In particular, the verification of softening of zone-centre acoustic phonons polarised along 〈110〉, and the use of microscopy techniques to characterise domain microstructure within the low-temperature ferroelastic phase will provide important experimental constraints on the phenomenology of what appears to be a canonical proper ferroelastic transition in a Fig. 6 (a) Representation of the crystal structure of ĳCuĲMeCN)Ĳtcm)], viewed away from a, as determined using single-crystal X-ray diffraction measurements carried out at 100 K. Thermal ellipsoids are drawn at 50% probability level. Panels (b) and (c) show topological representations of, respectively, this same framework and that of [Ag(MeCN) (tcm)] as reported in ref. 42. Both structures are assembled from honeycomb (6,3) nets of connected Cu/Ag cations and tcmanions. In (b) these nets stack such that the MeCN ligands of one net interdigitate the hexagonal channels of the next. In (c) pairs of adjacent nets interweave, with the MeCN groups occupying the space between adjacent honeycomb pairs. The corresponding unit cells for both systems are shown in black; the Cu/Ag and tcm components of two adjacent honeycomb nets (but not the coordinated MeCN groups) are shown in space-filling representation. MOF. The most obvious difference between the ferroelastic behaviour of Cu(tcm) and that of "conventional" systems such as As 2 O 5 is the very large strains realised within the ferroelastic phase [ Fig. 4(d)], as implied by the colossal thermal expansion.
Finally, the coordinative flexibility of Cu(tcm) is found to affect not only elastic behaviour but also the ability of the framework to reorganise itself on exposure to a coordinating solvent. In this way, we have demonstrated proof-of-principle for application of Cu(tcm) as an acetonitrile sensor. Given the diversity of known AgĲtcm)·{guest} phases, 27,42 the possibility that Cu(tcm) may respond selectively to a variety of different solvents offers an attractive avenue for further research.