Damian Paliwoda

Laure Vendier

Livia Getzner

Frederico Alabarse

Davide Comboni

Seyed Baptiste Martin

Ehsan Alavi

Mario Piedrahita Bello

Lionel Salmon

William Nicolazzi

Seyed Ehsan Alavi

Gábor Molnár

Azzedine Bousseksou

Elastic Properties of the Iron(II

come

INTRODUCTION

Certain (pseudo-)octahedral iron(II) complexes with N-donor ligands are known to undergo spincrossover (SCO) phenomenon triggered by temperature, light irradiation, intense magnetic field, guest molecules and/or applied pressure. [START_REF] Gütlich | Thermal and optical switching of iron (II) complexes[END_REF][2][START_REF]Fe(NH2trz)](NO3)2 (Htrz=1,2,4-4H-Triazole, trz=1,2,4-Triazolato)[END_REF][START_REF] Bousseksou | Molecular spin crossover phenomenon: recent achievements and prospects[END_REF] This reversible switching between the paramagnetic high spin (HS) and diamagnetic low spin (LS) states is known to be strongly influenced by electronlattice coupling, which often leads to cooperative behavior in the solid state, manifested notably by the emergence of first-order phase transitions with hysteresis loops. As a consequence of this bistability, switchable SCO molecules are very attractive and can potentially be used as components of memory devices, displays, sensors and actuators. [START_REF] Bousseksou | Molecular spin crossover phenomenon: recent achievements and prospects[END_REF][START_REF] Kumar | Emerging trends in spin crossover (SCO) based functional materials and devices[END_REF] Among the large variety of SCO compounds, one-dimensional, triazole-bridged iron(II) coordination polymers have received particular attention in the past decades. [START_REF] Roubeau | Triazole-Based One-Dimensional Spin-Crossover Coordination Polymers[END_REF][START_REF] Lavrenova | Spin crossover and thermochromism of iron(II) coordination compounds with 1,2,4-triazoles and tris (pyrazol-1-yl) methanes[END_REF][START_REF] Kahn | Iron (II)-1, 2, 4,-triazole spin transition molecular materials[END_REF][START_REF] Garcia | Spin crossover in 1D, 2D and 3D polymeric Fe (II) networks[END_REF][START_REF] Lavrenova | Spin transition in iron(II) complexes with 1,2,4-triazoles and tetrazoles[END_REF][START_REF] Koningsbruggen | Special classes of iron (II) azole spin crossover compounds[END_REF] These compounds of formulae [Fe(4-R-1,2,4-triazole)3][anion]2•nSolv (Solv = solvent molecules) consist of linear chains of ferrous ions linked by three N1,N2-1,2,4-triazole bridges. This short, rigid and stable linkage gives rise to unique properties with respect to other SCO compounds. First, its robustness provides a straightforward means to modify the triazole ligand at the 4-position (including even post-synthetic modifications [START_REF] Enríquez-Cabrera | Complete post-synthetic modification of a spin crossover complex[END_REF] ), providing access to a vast family of compounds. [START_REF] Roubeau | Triazole-Based One-Dimensional Spin-Crossover Coordination Polymers[END_REF] This versatility is further enhanced by the possibility of counter-anion substitutions as well as the inclusion of solvent molecules. As such, the SCO properties can be tuned to a great extent, affording for Fetriazole derivatives, which display SCO near and above room temperature. [START_REF] Roubeau | Triazole-Based One-Dimensional Spin-Crossover Coordination Polymers[END_REF][START_REF] Lavrenova | Spin crossover and thermochromism of iron(II) coordination compounds with 1,2,4-triazoles and tris (pyrazol-1-yl) methanes[END_REF][START_REF] Kahn | Iron (II)-1, 2, 4,-triazole spin transition molecular materials[END_REF][START_REF] Garcia | Spin crossover in 1D, 2D and 3D polymeric Fe (II) networks[END_REF][START_REF] Lavrenova | Spin transition in iron(II) complexes with 1,2,4-triazoles and tetrazoles[END_REF][START_REF] Koningsbruggen | Special classes of iron (II) azole spin crossover compounds[END_REF][START_REF] Enríquez-Cabrera | Complete post-synthetic modification of a spin crossover complex[END_REF][START_REF] Haasnoot | 1,2,4-Triazole Complexes, III. Complexes of Transition Metal(II) Nitrates and Fluoroborates[END_REF][START_REF] Lavrenova | Hightemperature spin transition in coordination compounds of iron (II) with triazoles (in Russian)[END_REF][16][START_REF] Sugiyarto | Cooperative Spin Transitions in Iron(II) Derivatives of 1,2,4-Triazole[END_REF][START_REF] Roubeau | Spin Transition Regime in New One-Dimensional Polymeric Iron(II) Compounds. Importance of the Water Content for the Thermal and Optical Properties[END_REF] Furthermore, the triazole bridge confers in many cases high cooperativity to these systems, manifested by large thermal hysteresis loops. These properties aroused tremendous interest since the pioneering works of Olivier Kahn for the technological use of this family of compounds. [START_REF] Kahn | Spin transition molecular materials for displays and data recording[END_REF][START_REF] Kahn | Spin-transition polymers: from molecular materials toward memory devices[END_REF] Due to notorious crystallization difficulties, most of the known triazole based iron(II) complexes are available only as polycrystalline materials, often of poor crystallinity. Despite the lack of single crystals, the chain type molecular structure of numerous iron-triazole complexes could be established very early using IR spectroscopy, [START_REF] Sheludyakova | IR spectral study of the 1A1⇄5T2 spin transition in Iron(II) complexes with 1,2,4-triazole[END_REF] EXAFS (extended X-ray absorption fine structure) [START_REF] Michalowicz | EXAFS and X-ray powder diffraction studies of the spin transition molecular materials[END_REF] and WAXS (wide angle X-ray scattering) [START_REF] Verelst | Structural Study by Wide-Angle X-ray Scattering of the Spin Transition Molecular Materials [Fe(Htrz)[END_REF] measurements as well as by comparison with analogous Cu(II)-triazole complexes, [START_REF] Haasnoot | Mononuclear, oligonuclear and polynuclear metal coordination compounds with 1,2,4-triazole derivatives as ligands[END_REF] providing suitable crystals for structural analysis. On this basis, it could be clearly established that in these compounds the iron(II) ion is surrounded by six triazole ligands, bridging it with two other metal ions and forming thus an infinite chain of iron-triazole units. More recently, a decisive progress could be achieved by solving the crystal structure of a few Fe(II) triazole complexes using either single-crystal X-ray diffraction [START_REF] Grosjean | The 1-D polymeric structure of the [Fe(NH2trz)3](NO3)2•nH2O (with n= 2) spin crossover compound proven by single crystal investigations[END_REF][START_REF] Grosjean | Matériaux polymériques 1D à transition de spin : investigations structurales multi-échelles[END_REF] or powder X-ray diffraction (PXRD) [START_REF] Grosjean | Crystal Structures and Spin Crossover in the Polymeric Material [Fe(Htrz)2(trz)](BF4) Including Coherent-Domain Size Reduction Effects[END_REF][START_REF] Sirenko | Direct Synthesis of Spin-Crossover Complexes: An Unexpectedly Revealed New Iron-Triazolic Structure[END_REF][START_REF] Nieto Castro | Advances in Spin Crossover: Synthesis, Mechanosynthesis and Switchable Multifunctional Hybrids[END_REF] techniques. In particular, two complexes, [Fe(NH2trz)3](NO3)2•nH2O [START_REF] Grosjean | The 1-D polymeric structure of the [Fe(NH2trz)3](NO3)2•nH2O (with n= 2) spin crossover compound proven by single crystal investigations[END_REF] and [Fe(NH2trz)3](BF4)(SiF6)0,5, [START_REF] Grosjean | Matériaux polymériques 1D à transition de spin : investigations structurales multi-échelles[END_REF] have been found suitable for detailed single crystal X-ray diffraction studies, though the former only in the LS state. The structural picture emerging from these efforts is nicely summarized in the PhD thesis of A.

Grosjean. [START_REF] Grosjean | Matériaux polymériques 1D à transition de spin : investigations structurales multi-échelles[END_REF] Despite a relatively similar organization, based on parallel chains of [Fe(R-trz)3]n, these compounds can crystallize in various crystal systems (triclinic, orthorhombic, trigonal and hexagonal). The HS and LS phases are often isostructural, though the generalization of this point certainly requires further work. Remarkably, all these different structures display a common lattice parameter of ca. 7.3-7.9 Å (c in hexagonal and trigonal systems, b in orthorhombic and a in triclinic), which is just twice the distance between the nearest Fe ions in the chains. Importantly, in a given spin-state, this distance appears similar in each compound, resulting always in a similarly large variation of the corresponding lattice parameter (~5-6 %). The two other cell parameters, reflecting the inter-chain distances, display values of ca. 9-10 Å (or their multiples), which depend in a subtle manner on the different inter-chain interactions involved (e.g. direct chain-chain or mediated by different anions and solvent molecules). Upon the LS to HS transition, these 'inter-chain lattice parameters' can display, however, strikingly different behaviors from one compound to other (e.g. increase, decrease or no change). It is worth noting also that the chains remain linear in the two spin states, but may exhibit relative movements (rotation/translation) among them. This important progress in the structural analysis of Fe(II)-triazole chain complexes opens new prospects also for the investigation of the elastic properties of these compounds, which is the scope of the present paper. On one hand, the elasticity of the crystal lattice appears important, as it plays a key role in the cooperativity of the spin transition. Indeed, since the pioneering works of Spiering et al. [START_REF] Spiering | The effect of the lattice expansion on high spin⇌ low spin transitions[END_REF][START_REF] Spiering | Elastic interaction in spin-crossover compounds[END_REF] it is commonly accepted in the SCO community that the cooperativity of the SCO is governed primarily by short-and long-range elastic interactions, which arise due to the change of the size and shape of the molecules. Furthermore, the recent advances in the use of these Fe-triazole compounds in mechanical transducers (e.g. actuators, 32 sensors 33 and harvesters [START_REF] Rat | Coupling mechanical and electrical properties in spin crossover polymer composites[END_REF] obviously calls for a better knowledge of their elastic properties.

Here, we focus on the compounds [Fe(Htrz)2trz]BF4 (1) and [Fe(NH3trz)3]SO4 (2) (Figure 1), which were chosen for two main reasons. First, they are among the scarce Fe-triazole SCO complexes whose crystal structure has been solved in both spin states. [START_REF] Grosjean | Crystal Structures and Spin Crossover in the Polymeric Material [Fe(Htrz)2(trz)](BF4) Including Coherent-Domain Size Reduction Effects[END_REF][START_REF] Sirenko | Direct Synthesis of Spin-Crossover Complexes: An Unexpectedly Revealed New Iron-Triazolic Structure[END_REF][START_REF] Nieto Castro | Advances in Spin Crossover: Synthesis, Mechanosynthesis and Switchable Multifunctional Hybrids[END_REF] Second, both compounds exhibit remarkable behavior when undergoing SCO with relatively wide hysteresis loops above room temperature, coupled with a large volume change. These appealing features make them very attractive for various applications. In the present study, we have first confirmed and completed existing knowledge about the change of lattice parameters in the course of the thermal SCO for both compounds, which was followed by the investigation of the lattice compressibility, using synchrotron PXRD under pressure. The temperature dependence of the elastic properties across the spin transition was then qualitatively assessed by means of dynamical mechanical analysis (DMA). Finally, the magnitude of elastic energy changes was evaluated in the context of differential scanning calorimetry (DSC) data, together with some other relevant thermodynamical properties.

EXPERIMENTAL SECTION

Sample preparation. Polycrystalline samples of [Fe(NH2trz)3]SO4 and [Fe(Htrz)2trz]BF4

were synthesized and characterized as described in previous reports. [START_REF] Piedrahita-Bello | 4D printing with spin-crossover polymer composites[END_REF][START_REF] Suleimanov | Effect of ligand substitution in [Fe(H-trz)2(trz)]BF4 spin crossover nanoparticles[END_REF] 2.2. High-temperature PXRD. X-ray powder patterns were recorded on a Rigaku Smartlab instrument using a Cu source (λ = 1.54056 Å) and a fast linear detector (D Tex Ultra 250). The diffractometer was used in a theta/theta configuration with a "Cross Beam Optics" parabolic mirror in Bragg-Brentano mode, a 1 mm incident slit and a 20 mm receiving slit. Data were recorded in the 5 -50° 2θ range (step: 0.02°, speed 1°/min), on heating and cooling between 20 -140 °C, in ambient air, using as high temperature chamber the Rigaku XRD-DSC accessory.

High-pressure PXRD.

High-pressure powder X-ray diffraction measurements were performed in two synchrotron X-ray facilities. [Fe(NH3trz)3]SO4 was investigated both at the High Pressure Diffraction beamline, Xpress of the Elettra Sincrotrone Trieste (using PILATUS3 S 6M DECTRIS detector and an X-ray wavelength λ = 0.4955 Å) and on the ID15b beamline at the European Synchrotron Radiation Facility (using Eiger2XE 9M CdTe DECTRIS detector and an X-ray wavelength λ = 0.4104 Å). The latter beamline was also used to investigate the [Fe(Htrz)2trz]BF4 complex. Each sample was loaded separately into a membrane-driven diamond anvil cell together with a small ruby sphere and topped with Daphne 7373 oil. [START_REF] Tateiwa | Evaluations of pressure-transmitting media for cryogenic experiments with diamond anvil cell[END_REF] The value of pressure was estimated before and after each XRD experiment from the shift in the R1 fluorescence line of ruby. [START_REF] Piermarini | Calibration of the pressure dependence of the R 1 ruby fluorescence line to 195 kbar[END_REF] In each case, the XRD images were converted to 1D diffraction profiles using Dioptas 39 and unit-cell parameters were refined using the LeBail 40 method, as implemented in the Jana2006 software. [START_REF] Petricek | Crystallographic Computing System JANA2006: General features[END_REF] 2.4. Dynamical mechanical analysis. DMA measurements were conducted between 10 and 130 °C at a heating/cooling rate of ±1 °C.min -1 by means of a DMA850 instrument (TA Instruments) equipped with a special sample holder for powders. [START_REF] Mahlin | A novel powder sample holder for the determination of glass transition temperatures by DMA[END_REF] The latter consists of two rectangular stainless steel pieces, among which the powder (ca. 50 mg) is disposed. The sample holder was mounted in a dual cantilever clamp and it was oscillated perpendicular to its base plane by a vertical motion of the middle clamp (see Fig. 2 and Scheme S1 in the Supporting Information, SI).

The measurements were conducted in constant strain mode with 0.08 % strain amplitude at different frequencies (1, 10 and 100 Hz). Each sample was measured through several thermal cycles to verify the reproducibility of the results. Owing to the powdery nature of the samples, absolute values of storage and loss moduli (E' and E") cannot be reliably assessed, but their variation provides relevant information on thermally induced changes of viscoelastic properties. 1) were determined and refined at 420 K and 300 K by Grosjean et al. [START_REF] Grosjean | Crystal Structures and Spin Crossover in the Polymeric Material [Fe(Htrz)2(trz)](BF4) Including Coherent-Domain Size Reduction Effects[END_REF] Compound 1 forms orthorhombic crystals, space group Pnma, in which the iron(II) ion lies on an inversion center and is coordinated by two Htrz and one trz bridging ligands (see Fig. 1a and1c).

The structure of the compound [Fe(NH2trz)3]SO4 (2) was assessed in the LS state by Sirenko et al. [START_REF] Sirenko | Direct Synthesis of Spin-Crossover Complexes: An Unexpectedly Revealed New Iron-Triazolic Structure[END_REF] and completed later with the HS state structure by Nieto-Castro [START_REF] Nieto Castro | Advances in Spin Crossover: Synthesis, Mechanosynthesis and Switchable Multifunctional Hybrids[END_REF] . Compound 2 crystallizes in the hexagonal P63/m space group with two formula units per cell. Similar to complex 1, the iron(II) ion is coordinated by six NH2-trz ligands bridging the neighboring metal centers (see Fig. We have performed a series of variable temperature PXRD experiments on both polycrystalline samples. Representative diffractograms in the two spin states are shown in Figure 3 and the main structural parameters are summarized in Table 1 (see Figures S1-S4 for a compilation of the ensemble of the experimental data). In the case of 1, a detailed variabletemperature PXRD analysis has been already reported by Grosjean et al. [START_REF] Grosjean | Matériaux polymériques 1D à transition de spin : investigations structurales multi-échelles[END_REF][START_REF] Grosjean | Crystal Structures and Spin Crossover in the Polymeric Material [Fe(Htrz)2(trz)](BF4) Including Coherent-Domain Size Reduction Effects[END_REF] and for this compound, our objective was thus merely to confirm if the sample in our hands displays the same behavior. However, no detailed temperature dependence was published for compound 2 and we report here the analysis of thermal strain in this material. As expected, at high temperatures, both complexes undergo a reversible transition from the LS to the HS form, accompanied with a large expansion of the unit cell volume (Figure 4a). Compound 1 expands its volume by nearly 11 %, the initially denser 2 only by 5 %. It is interesting to remark that the ordinary thermal dilation of the two compounds is rather small in all crystallographic directions and in both spin-states (see Fig. 4 and Fig. S5), characterized by linear thermal expansion coefficients of the order of 10 -5 K - 1 . The origin of this phenomenon requires further investigations, but it is worth to remark that zero or even negative thermal expansion is relatively frequent in network structures, [START_REF] Miller | Negative thermal expansion: a review[END_REF] and we can thus tentatively suggest that this might be a recurrent feature in Fe(II)-triazole chains as well. S1-S7). Both complexes show monotonic compressibility, although highly anisotropic behavior of unit-cell parameters has been revealed (Fig. 5). Third order Birch-Murnaghan equations of state were roughly fitted to the unit cell volume evolution of 1 and 2 with pressure using EosFit7. [START_REF] Angel | Equations of State[END_REF] The bulk modulus of 1 in the LS state is equal to 20 (±3) GPa, which is exceptionally high among other SCO complexes displaying values typically in the range between 5-12 GPa. [START_REF] Mikolasek | Complete Set of Elastic Moduli of a Spin-Crossover Solid: Spin-State Dependence and Mechanical Actuation[END_REF] Such low compressibility, combined with a large volume change at the SCO should explain the outstanding cooperativity of this compound. Against odds, the most compressive direction turns out to be the b-axis, along the chains. This unexpected finding stems likely from the compact lattice packing of 1, characterized by short inter-chain distances. Interestingly, a negative linear compressibility of parameter a is observed between ca. 2.2 and 3.5 GPa in this compound, which may suggest the rearrangement of the chain -anion interactions. and the drop of parameter c around 0.7 GPa in complex 2.

The bulk modulus of 2 is significantly lower, ca. 13 (±2) GPa, but can be considered still high in comparison with other SCO systems. [START_REF] Mikolasek | Complete Set of Elastic Moduli of a Spin-Crossover Solid: Spin-State Dependence and Mechanical Actuation[END_REF] In contrast to 1, where the most compressible unit-cell parameter is the one along the chains, complex 2 manifests the opposite behavior with the parameter c being the least compressible. One must note, however, that an anomalous behavior of parameter c has been detected between ca. 0.59 and 0.83 GPa, which was also confirmed in a second series of experiments performed at Elettra Sincrotrone Trieste. This discontinuity suggests the occurrence of a structural transition, which should be confirmed by structural refinements (out of the scope of the present paper). We just note here that in the low-pressure range (< 0.6 GPa) the compressibility of 2 seems actually fairly isotropic (within the experimental uncertainties).

Dynamical mechanical analysis.

Besides the room temperature elastic moduli, the temperature dependence of elastic properties across the spin transition is of considerable interest as well. To investigate this question, we conducted variable temperature DMA measurements. In general, DMA tests require 'compact', freestanding samples (e.g. pellets, films, large crystals), which can be investigated in tension, compression, bending or shear configurations. However, the SCO phenomenon is notoriously sensitive to mechanical treatments and pelletizing does not appear as a good option. [START_REF] Gütlich | Thermal and optical switching of iron (II) complexes[END_REF] Another possibility is to embed the SCO particles in a suitable matrix, enabling to fix the geometry of the sample as a composite film. This strategy is more promising, but the extraction of the particle viscoelastic properties is not straightforward and the matrix might also affect the SCO properties of the particles. [START_REF] Bousseksou | Molecular spin crossover phenomenon: recent achievements and prospects[END_REF] We have thus decided to analyze directly the neat polycrystalline samples. At this point, it is important to underline that the complex dynamical moduli obtained from DMA on such loose powder samples remains only a qualitative measure of their viscoelastic behaviors. In particular, the magnitude of the storage modulus (E') is dominated by the steel sample holder (see Fig. 1) and its absolute value cannot be easily interpreted. On the other hand, since steel behaves elastically in the temperature range of our interest, any step transition of E' or peak in the loss tangent (tan) should be interpreted as a thermally induced phenomenon in the powder sample. Indeed, this approach has been successfully used in the past to investigate glass and melting transitions in various powder samples. [START_REF] Mahlin | A novel powder sample holder for the determination of glass transition temperatures by DMA[END_REF][START_REF] Pinheiro | Study of the glass transition on viscous-forming and powder materials using dynamic mechanical analysis[END_REF][START_REF] Kissi | Glass-Transition Temperature of the β-Relaxation as the Major Predictive Parameter for Recrystallization of Neat Amorphous Drugs[END_REF][START_REF] Xiao | Linking Glass-Transition Behavior to Photophysical and Charge Transport Properties of High-Mobility Conjugated Polymers[END_REF] Representative data for E' and tan, recorded on heating and cooling are shown in Figure 6 for our two powder samples (see also Figures S12-S13 in the SI). For both samples, tan exhibits distinct peaks at the spin transition, which indicates, as it can be expected, [START_REF] Pérez-Sáez | Anelastic contributions and transformed volume fraction during thermoelastic martensitic transformations[END_REF][START_REF] Jackson | Properties of rocks and minerals: physical origins of anelasticity and attenuation in rock[END_REF] enhanced internal frictions in the course of the spin transition. At a first glance, the temperature dependence of the storage modulus of sample 1 exhibits a reversible increase when going from the LS to the HS state (Fig. 6a)in close resemblance with our previous DMA measurements on polymer composite films containing particles of 1. [START_REF] Rat | Elastic coupling between spin-crossover particles and cellulose fibers[END_REF] In the case of the composite samples, we argued that the counter-intuitive increase of the stiffness in the HS phase might arise from the increase of the particle volume fraction in the composite material.

The present results on the neat powder sample clearly invalidate our previous hypothesis.

Nonetheless, a stiffening of the particles in the less dense HS phase appears unphysical. A first explanation for this apparent discrepancy comes from the DMA analysis of sample 2 (Fig. 6b), which points more clearly to the existence of a dip of E' around the spin transition temperatureinstead of a step-like change. In other words, the elastic modulus changes observed in our experiments do not reflect the difference of the 'normal' stiffness of the two phases. Instead, they arise due to the spin transition itself. Similar to other types of phase transitions, [START_REF] Carpenter | Elastic anomalies in minerals due to structural phase transitions[END_REF] and in-line with previously reported resonant ultrasonic spectroscopy measurements on a few molecular SCO compounds [START_REF] Mason | Structural and spectroscopic characterisation of the spin crossover in[END_REF][START_REF] Jakobsen | Domain Wall Dynamics in a Ferroelastic Spin Crossover Complex with Giant Magnetoelectric Coupling[END_REF][START_REF] Dobbelaar | Thermal and Magnetic Field Switching in a Two-Step Hysteretic MnIII Spin Crossover Compound Coupled to Symmetry Breakings[END_REF] and static compression of iron-bearing minerals, [START_REF] Wu | Anomalous thermodynamic properties in ferropericlase throughout its spin crossover[END_REF] we therefore suggest that the elastic softening at the spin transition observed in our experiments should be induced by the coupling of the spin-state of the molecules to lattice strains. Indeed, when an SCO material is subjected to an external stress, as in a DMA experiment, it will deform to some extent, which depends on its elastic constants. However, a change in the strain state of the material will result in a change of the HS-LS equilibrium, because it affects the free energy of the HS and LS phases unequally. Specifically, tensile strains will favor the HS form, which has higher volume, whereas compression has the opposite effect. The material will thus adjust its spin state in response to the applied external stress until new equilibrium is reached. The spin-state of the system provides thus an additional, indirect and time-dependent (anelastic) link between stress and strain, in addition to the ordinary instantaneous (elastic) response. [START_REF] Nowick | Anelastic relaxation in crystalline solids[END_REF] This relaxation of the spin state of the system acts to facilitate the deformation, because the SCO also contributes to the change of strain state. Hence, the material appears effectively softer than it would be in the absence of this relaxation. In addition, since the relaxation process is irreversible, energy is dissipated and there will be thus a phase lag between stress and strain, which depends on the relaxation time of the system and the frequency of the applied stress. Cases in which the SCO occurs via phase separation, i.e. first-order transitions, offer more complications due to the fact that the applied stress may move the HS/LS interface(s), in addition to changing the local equilibrium of the system. Further, when the SCO crystallite is embedded in a matrix of other particles, other damping mechanisms might arise, such as grain boundary relaxation. [START_REF] Nowick | Anelastic relaxation in crystalline solids[END_REF] Before moving to a more formal analysis of this elastic softening phenomenon, we shall discuss our experimental observations regarding the mechanical loss behavior, seen as peaks of tan at the spin transition (Fig. 6). These loss peaks do not exhibit the same large asymmetry as the storage modulus patterns and they coincide with the point of the largest slope in the E'(T) curve (indicated by dashed vertical lines in Fig. 6). This point should correspond thus to the spin transition temperature, where the spin state of the material is the most sensitive to any change of external stress. Further, variable frequency (1-100 Hz) and variable temperature rate (1-3 K/min) DMA measurements revealed that the amplitude of mechanical loss peaks are clearly reduced at increasing frequencies and lower scan rates (Fig. 6c-6d), which was reproducibly observed in our experiments. Importantly, one should also notice that the loss peaks do not shift with changing frequency, something unusual for a relaxation process, but it is actually a general feature of anelastic relaxations, which arise due to phase transitions. [START_REF] Nowick | Anelastic relaxation in crystalline solids[END_REF] One might wonder that besides the spin-state relaxation, which is thought to govern the elastic softening, some additional damping mechanisms might exist. Indeed, such low-frequency (~1 Hz) mechanical responses at first-order phase transitions are usually associated with interfacial phenomena, [START_REF] Nowick | Anelastic relaxation in crystalline solids[END_REF] which could be internal frictions at HS/LS phase boundaries in our case. Nevertheless, it is worth mentioning that pronounced loss peaks at the SCO were reported previously at much higher frequencies in resonant ultrasound spectroscopy experiments [START_REF] Mason | Structural and spectroscopic characterisation of the spin crossover in[END_REF][START_REF] Jakobsen | Domain Wall Dynamics in a Ferroelastic Spin Crossover Complex with Giant Magnetoelectric Coupling[END_REF][START_REF] Dobbelaar | Thermal and Magnetic Field Switching in a Two-Step Hysteretic MnIII Spin Crossover Compound Coupled to Symmetry Breakings[END_REF] (~1 MHz) and MEMS based measurements 58 (~50 kHz) even for materials displaying continuous transitions, for which no phase separation is expected.

Further investigations over a broad range of frequencies and temperatures will be thus indispensable to properly 'map' the anelastic response of SCO materials. [START_REF] Carpenter | Anelasticity maps for acoustic dissipation associated with phase transitions in minerals[END_REF] As discussed in detail by Carpenter and Salje, [START_REF] Carpenter | Elastic anomalies in minerals due to structural phase transitions[END_REF] to calculate the elastic constant variations at a phase transition, the excess Gibbs free energy ∆𝐺 𝑒𝑥𝑐𝑒𝑠𝑠 can be written in terms of a Landau potential, 𝐿(𝜂), the elastic strain energy, ∆𝐺 𝑒 (𝜀), and the coupling energy, ∆𝐺 𝑐 (𝜂, 𝜀), as:

∆𝐺 𝑒𝑥𝑐𝑒𝑠𝑠 = 𝐿(𝜂) + ∆𝐺 𝑐 (𝜂, 𝜀) + ∆𝐺 𝑒 (𝜀) = 𝐿(𝜂) + ∑ 𝜆 𝑖,𝑚,𝑛 𝜀 𝑖 𝑚 𝜂 𝑛 𝑖,𝑚,𝑛 + 1 2 ∑ 𝐶 𝑖𝑗 °𝑖𝑗 𝜀 𝑖 𝜀 𝑗 (Eq. 1)
The first term L(𝜂) accounts for the contributions from the order parameter 𝜂 alone. The second term describes the interaction between the order parameter and the transformation strains 𝜀 𝑖 (in Voigt notation), where 𝜆 𝑖,𝑚,𝑛 is the strain -order parameter coupling coefficient. Finally, the last term accounts for the elastic energy, where 𝐶 𝑖𝑗 ° are the relevant elastic constants of the highsymmetry phase. The exponents m and n depend on the symmetry properties of 𝜂 and . In the case of an isostructural spin transition, the 'Landau term' can be written, as discussed by Chernyshov [START_REF] Chernyshov | Landau theory for spin transition and ordering phenomena in Fe (II) compounds[END_REF] and Collet [START_REF] Azzolina | General Landau theory of non-symmetry-breaking and symmetry-breaking spin transition materials[END_REF][START_REF] Collet | Coupling and decoupling of spin crossover and ferroelastic distortion: Unsymmetric hysteresis loop, phase diagram, and sequence of phases[END_REF] , as:

𝐿(𝜂) = 𝐴𝜂 𝑠𝑝𝑖𝑛 + 1 2 𝐵𝜂 𝑠𝑝𝑖𝑛 2 + 1 4 𝐶𝜂 𝑠𝑝𝑖𝑛 4 (Eq. 2)
where 𝐴 = 𝑎(𝑇 𝑆𝐶𝑂 -𝑇), B and C are the phenomenological parameters of the Landau potential, and 𝜂 𝑠𝑝𝑖𝑛 , the totally symmetric order parameter, is given by the number N of HS and LS molecules (or, alternatively, by the fraction of LS molecules 𝑛 𝐿𝑆 ) as:

𝜂 𝑠𝑝𝑖𝑛 = 𝑁 𝐻𝑆 -𝑁 𝐿𝑆 𝑁 𝐻𝑆 +𝑁 𝐿𝑆 = 1 -2𝑛 𝐿𝑆 (Eq. 3)
𝜂 𝑠𝑝𝑖𝑛 transforms as the identity representation and takes values between -1 (LS) and +1 (HS). In the following, let us consider the case of compound 2 with a hexagonal P63/m structure, for which symmetry, the combination of Equations 1 and 2 gives:

∆𝐺 𝑒𝑥𝑐𝑒𝑠𝑠 = 𝐴𝜂 𝑠𝑝𝑖𝑛 + 1 2 𝐵𝜂 𝑠𝑝𝑖𝑛 2 + 1 4 𝐶𝜂 𝑠𝑝𝑖𝑛 4 + 𝜆 1 𝑛 𝐿𝑆 (𝜀 1 + 𝜀 2 ) + 𝜆 2 𝑛 𝐿𝑆 𝜀 3 + 𝜆 3 𝑛 𝐿𝑆 (𝜀 4 2 + 𝜀 5 2 ) + +𝜆 4 𝑛 𝐿𝑆 [𝜀 6 2 + (𝜀 1 -𝜀 2 ) 2 ] + 1 4 (𝐶 11 °+ 𝐶 12 °)(𝜀 1 + 𝜀 2 ) 2 + 1 4 (𝐶 11 °-𝐶 12 °)(𝜀 1 -𝜀 2 ) 2 + 𝐶 13 °(𝜀 1 + 𝜀 2 )𝜀 3 + 1 2 𝐶 33 °𝜀3 2 + 1 2 𝐶 44 °(𝜀 4 2 + 𝜀 5 2 ) + 1 2 𝐶 66 °𝜀6 2 (Eq. 4)
As a first approximation, only the lowest order symmetry-allowed couplings are considered in Equation 4, which are bilinear for the non-symmetry-breaking strains (𝜀 1 =𝜀 2 , 𝜀 3 ) and linearquadratic for the symmetry-breaking strains (𝜀 4 = 𝜀 5 = 𝜀 6 = 0). To derive the temperature dependence of the elastic constants 𝐶 𝑖𝑗 , for which 𝑖, 𝑗 = 1 -3, one can conveniently use the formula: 52

𝐶 𝑖𝑗 = 𝐶 𝑖𝑗 °-𝜕 2 𝐺 𝜕𝜀 𝑖 𝜕𝑛 𝐿𝑆 𝜒 𝜕 2 𝐺 𝜕𝑛 𝐿𝑆 𝜕𝜀 𝑗 (Eq. 5)
wherein the so-called order parameter susceptibility, 𝜒, is given by:

𝜒 = ( 𝜕 2 𝐿 𝜕𝜂 𝑠𝑝𝑖𝑛 2 ) -1 = 1 𝐵+3𝐶𝜂 𝑠𝑝𝑖𝑛 2 (Eq. 6)
Applying equation 5 on equation 4, one obtains the following variations of elastic constants:

𝐶 11 = 𝐶 22 = 𝐶 11 °-𝜆 1 2 𝜒 (Eq. 7a)
𝐶 33 = 𝐶 33 °-𝜆 2 2 𝜒 (Eq. 7b)

𝐶 12 = 𝐶 12 °-𝜆 1 2 𝜒 -2𝜆 4 𝑛 𝐿𝑆 (Eq. 7c)

𝐶 13 = 𝐶 23 = 𝐶 13 °-𝜆 1 𝜆 2 𝜒 (Eq. 7d)

The remaining elastic constants are obtained as:

𝐶 44 = 𝐶 55 = 𝜕 2 𝐺
𝜕𝜀 4 2 = 𝐶 44 °+ 2𝜆 3 𝑛 𝐿𝑆 (Eq. 9)

𝐶 66 = 𝜕 2 𝐺 𝜕𝜀 4 2 = 𝐶 66 °+ 2𝜆 4 𝑛 𝐿𝑆 = 1 2
(𝐶 11 -𝐶 12 ) (Eq. 10)

The shear modulus, determined primarily by the behaviors of 𝐶 44 and 𝐶 66 , is therefore expected to show a stepwise evolution, mirroring the behavior of 𝑛 𝐿𝑆 (T). On the other hand, the bulk modulus behavior is dictated by the evolution of 𝐶 11 , 𝐶 12 , 𝐶 13 and 𝐶 33 . Indeed, equations 7a-7d predict a classical elastic softening behavior of the bulk modulus of 2, wherein the variation of the relevant elastic constants, ∆𝐶 𝑖𝑗 , is proportional to the square of the elastic coupling strength, 𝜆 2 and the order parameter susceptibility, 𝜒 (i.e. the shape of the Landau potential). [START_REF] Carpenter | Elastic anomalies in minerals due to structural phase transitions[END_REF] At this stage, it is important to remark that the storage modulus measured by DMA on our loose powder samples should contain contributions from both the shear and the bulk moduli of the particles, but in a way, which is difficult to predict by computations. As such, the experiments reflect only in a qualitative manner the softening of certain elastic constants at the spin transition, which is predicted by theory. For a quantitative link, further experiments on single crystal samples will be indispensable.

Calorimetric analysis.

Since the pioneering works of Sorai and Seki, 63-64 calorimetric techniques have been extensively used to investigate the enthalpy and entropy changes associated with the SCO phenomenon. Particular attention is devoted to the analysis of vibrational entropy changes, which are considered as the main driving force of the thermally induced SCO. [START_REF] Bousseksou | Raman spectroscopy of the high-and low-spin states of the spin crossover complex Fe(phen)2(NCS)2: an initial approach to estimation of vibrational contributions to the associated entropy change[END_REF][START_REF] Molnár | Molecular spin crossover materials: Review of the lattice dynamical properties[END_REF] However, in analogy with the martensitic transition in shape memory alloys, [START_REF] Wollants | Thermally-and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics[END_REF][START_REF] Torra | Martensitic transformations in shape-memory alloys: successes and failures of thermal analysis and calorimetry[END_REF][START_REF] Yawny | Entropy production in single-crystal single-interface martensite transformation[END_REF][START_REF] Isola | Effect of the precipitates on the thermodynamics of the martensitic transformations in Ti-rich Ni-Ti-Co thin films[END_REF] it appears interesting to discuss the calorimetric data with respect to the various thermo-elastic phenomena taking place in SCO materials.

To a first approximation, the mean value of the exchanged heat upon the forward (HSLS) and reverse (LSHS) transitions can be considered equal to the transformation enthalpy: Neglecting rotational and configurational degrees of freedom, the vibrational entropy can then be calculated as a difference of the total entropy change and electronic entropy change -taking only the spin multiplicity ratio (

) of the HS and LS states of the ferrous ions: 63

∆𝑆 𝑆𝐶𝑂 𝑣𝑖𝑏 = ∆𝑆 𝑆𝐶𝑂 -∆𝑆 𝑆𝐶𝑂 𝑠𝑝𝑖𝑛 ≈ ∆𝐻 𝑆𝐶𝑂 𝑇 𝑒𝑞 -𝑅𝑙𝑛( 5 1
) (Eq. 12)

Table 2 summarizes the calculated data for the two compounds, which are found in good agreement with previous reports. [START_REF] Sirenko | Direct Synthesis of Spin-Crossover Complexes: An Unexpectedly Revealed New Iron-Triazolic Structure[END_REF] In particular, one can note the significant vibrational entropy contribution (ca. 80 %), which provides the main driving force for the thermal spin transition in these materials. From the data in Fig. 5b, the elastic constant 𝐶 33 ° can be roughly estimated comparable with the bulk modulus (ca. 13 GPa), giving ∆𝐺 𝜀 ≈ 3 kJ/mol, i.e. ~15 % of the latent heat. It seems likely that this contribution is even higher in compound 1, which is not only sizably stiffer, but displays much higher strain contributions as well.

Another useful way to analyze the calorimetric data is based on the distinction between chemical and non-chemical energies that drive the transition. [START_REF] Wollants | Thermally-and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics[END_REF][START_REF] Torra | Martensitic transformations in shape-memory alloys: successes and failures of thermal analysis and calorimetry[END_REF][START_REF] Yawny | Entropy production in single-crystal single-interface martensite transformation[END_REF][START_REF] Isola | Effect of the precipitates on the thermodynamics of the martensitic transformations in Ti-rich Ni-Ti-Co thin films[END_REF] The main driving force for the spin transition is the chemical free energy difference (∆𝐺 𝑐ℎ𝑒𝑚 ) between the HS and LS phases:

∆𝐺 𝑐ℎ𝑒𝑚 = ∆𝐻 𝑆𝐶𝑂 -𝑇∆𝑆 𝑆𝐶𝑂 = (𝑇 -𝑇 𝑒𝑞 )∆𝑆 𝑆𝐶𝑂 (Eq. 14)

However, the fact that the heat of transformation is exchanged with the surroundings at different temperatures (𝑇 𝑆𝐶𝑂 LS  HS and 𝑇 𝑆𝐶𝑂 HS  LS ) is responsible for entropy production, since the same amount of heat absorbed at high temperature is released then at a lower temperature. An irreversible thermodynamical work, coined in the literature as 'frictional work', Wf, , must be thus involved in the transition process, which opposes both the forward and reverse transformations and is therefore responsible for the entropy production. [START_REF] Wollants | Thermally-and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics[END_REF] The actual operative mechanisms of this dissipation phenomenon (sic 'hysteresis loss') are not known for SCO materials, but in analogy with other phase change materials it should be related to interfacial phenomena and might also involve the emission of acoustic waves. [START_REF] Beke | Determination of elastic and dissipative energy contributions to martensitic phase transformation in shape memory alloys[END_REF] Nevertheless, even without the knowledge of the exact mechanisms, the thermodynamics frame can be discussed. The frictional work consumes the available driving force, and therefore the chemical free energy represents, according to the second law of thermodynamics, an upper limit to Wf such as: [START_REF] Wollants | Thermally-and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics[END_REF] ∆𝐺 = (𝑇 𝑡𝑟 -𝑇 𝑒𝑞 )∆𝑆 𝑆𝐶𝑂 ≥ 𝑊 𝑓 (Eq. 15)

where 𝑇 𝑡𝑟 = 𝑇 𝑆𝐶𝑂 HS  LS and 𝑇 𝑡𝑟 = 𝑇 𝑆𝐶𝑂 LS  HS for the forward and reverse transitions, respectively. For compounds 1 and 2 we can thus estimate the upper limit of frictional work as 1.2 and 0.6 kJ/mol, respectively, which is roughly 3-4 % of the latent heat.

Since the SCO phenomenon is accompanied by the change of shape and volume of the particles, elastic energy might be stored and released by the sample during the transformation. In a stress-free, high quality single-crystal, this stored elastic energy should be negligible. [START_REF] Beke | Determination of elastic and dissipative energy contributions to martensitic phase transformation in shape memory alloys[END_REF] On the contrary, in polycrystalline samples nucleation takes place in a randomly oriented particle matrix, which is not free from internal stresses. The growth of the nucleated phase will be arrested by grain boundaries and other obstacles within the solid matrix. To overcome the opposing stresses exerted by the surroundings, some additional overcooling/overheating is needed in order to increase the driving force. Because of this 'internal mechanical work', We, made by the transforming material, elastic energy will be stored during the forward transition and released in the reverse process. Due to this stored elastic energy, the latent heats of transformation are decreased for both processes.

The driving force consumed between the point when the transition starts (𝑇 𝑠𝑡𝑎𝑟𝑡 HS  LS ) and ends (𝑇 𝑒𝑛𝑑 HS  LS ) provides an upper limit to We: 67 The corresponding temperature values are tabulated in Tables S10 in the SI and the estimated upper limits of We are given in Table 2. The calculated values are rather small, ca. 2 % of the latent heat, indicating that stored elastic energies are negligible in these samples. It should be noted that the actual value of We is probably even smaller than this upper limit. In fact, small compositional, structural and microstructural heterogeneities among the powder particles must contribute to the widening of the transition region (𝑇 𝑒𝑛𝑑 -𝑇 𝑠𝑡𝑎𝑟𝑡 ), which limits of course the validity of a quantitative conclusion about the magnitude of 𝑊 𝑒 . At this point, it is worth to remind also that ∆𝐺 𝑐ℎ𝑒𝑚 is a material property, depending primarily on chemical composition and crystal structure, whereas 𝑊 𝑒 and 𝑊 𝑓 are strongly altered by microstructure. Finally, we shall underline that the above considerations refer to constant, atmospheric pressure and implicitly assume that the normal heat capacities of the two phases are equal (∆𝐶 𝑝 = 𝐶 𝑝 𝐻𝑆 -𝐶 𝑝 𝐿𝑆 = 0), which is never fully true.

Indeed, the excellent cycling reproducibility of the DSC thermograms in our samples allows to assess the exchanged heat in a complete cycle (∮ 𝑑𝑞), which turns out to be non-zero, the area of the forward transition peak being systematically smaller than that of the reverse transition (see Tables S8-S9). The most likely source of this non-zero value of ∮ 𝑑𝑞 is the heat capacity difference between the two phases: 67 which allows us to estimate the values of ∆𝐶 𝑝 for samples 1 and 2 as ~18 and ~6 J/K.mol, respectively. These values are comparable with the value of 18.7 J/K.mol measured by Sorai and Seki for the compound Fe(1,10-phenanothroline)2(NCS)2 using an adiabatic calorimeter. 63

CONCLUSIONS

In this paper we have assessed some fundamental thermo-elastic properties of two benchmark Fetriazole SCO complexes. The main findings and prospects are summarized below:

(1) The ordinary thermal expansion was found rather low in both compounds and it was suggested that this might be a general feature in this family of coordination networks.

(2) The transformation strain associated with the SCO is very anisotropic. In line with previous reports, [START_REF] Grosjean | Matériaux polymériques 1D à transition de spin : investigations structurales multi-échelles[END_REF][START_REF] Grosjean | Crystal Structures and Spin Crossover in the Polymeric Material [Fe(Htrz)2(trz)](BF4) Including Coherent-Domain Size Reduction Effects[END_REF] the largest expansion occurs along the Fe-triazole chains with values of ca. 5 -6.5 %, similar to other members of the family. This property is crucial for mechanical applications, because it means that different members of this family should provide the same, large amount of

Figure 1 .

 1 Figure 1. One-dimensional chains (a-b) and crystal packing (c-d) of the triazole-based iron(II) coordination polymers [Fe(Htrz)2trz]BF4 (a, c) 27 and [Fe(NH2trz)3]SO4 (b, d). 28 Counter-ions have

2. 5 .

 5 Differential scanning calorimetry. DSC thermograms were acquired using a Netzsch DSC 3500 Syrius instrument with a heating/cooling ramp of ±10 °C/min and a nitrogen gas purge of 20 mL/min. The samples were placed in a standard aluminum sample pan. Temperature and enthalpy were calibrated using the melting transition of indium.

Figure 2 . 3 . 1 .

 231 Figure 2. Scheme of the DMA setup using a dual cantilever clamp with a powder sample holder

  1b and 1d). Both structures are based on short intermolecular interactions between positively charged iron(II)-triazole chains and counter-anions. The packing of 1 is mostly governed by N-H(H-triazole) •••N(triazole) interchain hydrogen bonds and CH(triazole) •••F(anion) anion-chain interactions, while in compound 2 the anion-chain interactions become even stronger. This is due to the bulkier ligand obtained by the introduction of the NH2-group on the triazole moiety. Nevertheless, the amino group is also involved in the formation of inter-chain interactions. Besides, each [Fe(NH2trz)3]n chain is connected with the sulphate ion via N-H(aminogroup)•••O hydrogen bonds and short SO4 anion•••π(triazole ligand) interactions.

Figure 3 .

 3 Figure 3. Representative PXRD patterns of complexes 1 (a) and 2 (b) in the LS and HS states.

Figure 4 .

 4 Figure 4. Thermal expansion of the complexes: (a) comparison of the relative volume change in

Figure 5 .

 5 Figure 5. Pressure-induced unit cell transformations of complexes 1 (a) and 2 (b). Dotted lines

Figure 6 .

 6 Figure 6. Temperature dependence of the storage modulus and loss tangent for 1 (a) and 2 (b)

Figure 7

 7 Figure7shows the DSC curves acquired for samples 1 and 2 on five successive heating-

Figure 7 .

 7 Figure 7. DSC thermograms of powder samples of 1 (a) and 2 (b) acquired upon heating and

2 ≈

 2 ∆𝐻 𝑆𝐶𝑂 = 𝐻 𝐻𝑆 -𝐻 𝐿𝑆 = 𝑇 𝑒𝑞 ∆𝑆 𝑆𝐶𝑂 (Eq. 10) wherein the equilibrium temperature (∆𝐺 𝑆𝐶𝑂 (𝑇 𝑒𝑞 ) = 0) is roughly approximated by:

  HS  LS -𝑇 𝑠𝑡𝑎𝑟𝑡 HS  LS )∆𝑆 𝑆𝐶𝑂 ≥ 𝑊 𝑒 (Eq. 16)

17

 17

  )

Table 1 .

 1 PXRD-derived unit-cell parameters obtained for polycrystalline forms of compounds 1 and 2 in the two spin states.

	Compound	[Fe(Htrz)2(trz)]BF4 (1)	[Fe(NH2trz)3]SO4 (2)
	Molecular weight (g/mol)	348.8	407.1
	Spin state	LS	HS	LS	HS
	Temperature (°C)	44	129	24	109
	Space group, Z	Pnma, 4	Pnma, 4	P63/m, 2	P63/m, 2
	a (Å)	17.24(1)	17.32(3)	10.071(1)	10.05(1)
	b (Å)	7.353(8)	7.89(2)	10.071(1)	10.05(1)
	c(Å)	9.165(8)	9.49(2)	7.378(1)	7.75(1)
	α, β, γ (°)	90, 90, 90 90, 90, 90 90, 90, 120 90, 90, 120
	V (Å 3 )	1161(2)	1296(4)	648.03(17)	678(2)
	d (g/cm 3 )	1.995	1.788	2.086	1.994

Table 2 .

 2 Thermodynamical parameters extracted from DSC measurements for samples 1 and 2

	Sample	∆𝐻 𝑆𝐶𝑂 kJ/mol	∆𝐺 𝜀 kJ/mol	∆𝑆 𝑆𝐶𝑂 J/(K.mol)	𝑣𝑖𝑏 J/(K.mol) ∆𝑆 𝑆𝐶𝑂	Wf kJ/mol	Wel kJ/mol	Cp J/(Kmol)
	1	26.8	-	74.6		61.2		≤ 1.2	≤ 0.5	~18
	2	19.5	~3	58.2		44.8		≤ 0.6	≤ 0.4	~6
	Another interesting parameter we can extract from our experimental data is the elastic potential
	energy (∆𝐺 𝜀 ) contribution to the latent heat. In compound 2, the spontaneous strain of the spin
	transition contains only one component, namely, 𝜀 3 . The elastic energy contribution can be
	therefore calculated simply by:
				∆𝐺 𝜀 =	1 2	𝐶 33 °𝜀3	2		(Eq. 13)

ACKNOWLEDGMENTS

This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 101019522). The purchase of the SMARTLAB instrument was financed by the PRRI project Nanomat 2020 through the European Regional Development Fund and the Region Occitanie. The high-pressure X-ray

strain -provided the particles can be preferentially oriented. On the contrary, the strain contributions along the other lattice directions are very dissimilar in the two compounds (4 % in 1 and 0 % in 2) as they depend on intricate details of inter-chain interactions.

(3) The bulk moduli of both compounds are relatively high, with an outstanding 20 GPa value for 1 and 13 GPa for 2. This property, together with the large strains, must be at the origin of the high cooperativity of the SCO in these compounds. This combination of stiffness and strain provides large elastic potential energies, which could be estimated in 2 as high as 15 J/cm 3 (3 kJ/mol), amounting to ca. 15 % of the latent heat. Predictably, the lattice compressibility was found anisotropic, but unexpectedly the Fe-triazole axis turns out to be the most compressible in 1.

(4) DMA measurements revealed significant elastic softening and associated mechanical losses at the spin transition, which we interpreted as a consequence of the coupling of molecular spin-states to lattice strains. Similar to other types of phase transitions, [START_REF] Carpenter | Elastic anomalies in minerals due to structural phase transitions[END_REF] the strain -spin state coupling coefficients determine the magnitude of changes of the different elastic constants, whereas the shape of these anomalies reflects primarily the order parameter susceptibility. Further work is needed to evaluate the impact(s) of these anelastic phenomena on mechanical applications.

To this aim, more quantitative measurements should be conducted in a broad frequency and temperature window on single crystals displaying different SCO behaviors.

(5) Inspired by the vast literature on thermally-induced martensitic transformations, [START_REF] Wollants | Thermally-and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics[END_REF] we exploited the very robust calorimetric data of our compounds to quantify different thermo-elastic aspects of the SCO phenomenon, such as the stored elastic energy and the dissipated frictional