Impact of the Copper-Induced Local Framework Deformation on the

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Impact of the Copper-Induced Local Framework Deformation on the Mechanism of Structural Phase Transition In [(CH)NH][Zn(HCOO)] Hybrid Metal-Formate Perovskite 3

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Paulina Peksa, Justyna Trzmiel, Katarzyna Fedoruk, Anna G#gor, Mantas Šim#nas, Aneta Ciupa, Sebastian Pawlus, Juras Banys, Miroslaw Maczka, and Adam Sieradzki J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 03 Sep 2019 Downloaded from pubs.acs.org on September 3, 2019

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Impact of the Copper-Induced Local Framework Deformation on the Mechanism of Structural Phase Transition in [(CH3)2NH2][Zn(HCOO)3] Hybrid Metal-Formate Perovskite Paulina Peksa1, Justyna Trzmiel1, Katarzyna Fedoruk1, Anna Gągor2, Mantas Šimėnas3, Aneta Ciupa2, Sebastian Pawlus4, Juras Banys3, Mirosław Mączka2 and Adam Sieradzki1* 1.

Faculty of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

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Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Box 1410, 50-950 Wrocław 2, Poland

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Faculty of Physics, Vilnius University, Sauletekio 9, LT-10222 Vilnius, Lithuania

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Institute of Physics, University ofSilesian, ul. 75 Pułku Piechoty 1, 41-500 Chorzów, Poland

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email: [email protected]

ABSTRACT: Dimethylammonium zinc formate[(CH3)2NH2][Zn(HCOO)3] (DMAZn) treated as a model dense metal-organic framework is a compound being intensively studied in the last decade. It undergoes a first order order-disorder structural phase transition at T0~166 K, considered as the improper ferroelectric one. The complex mechanism of this phase transition is attributed to the ordering of the hydrogen bonds between (CH3)2NH2+ (DMA+) and the formate groups as well as distortion of the zinc-formate framework. Here the analysis of the

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impact of zinc substitution by Cu doping on the order-disorder phase transition is presented. The Jahn-Teller effect of Cu2+ ions results in a local framework distortion, which consequently perturbs the structural dynamics. Based on the dielectric, thermal, structural, electron paramagnetic resonance and IR spectroscopy measurements it is shown that doping with Cu2+ ions leads to a decrease of the phase transition entropy and temperature as well as the change of the character of the phase transition.

1. Introduction Hybrid coordination polymers crystallizing in a perovskite-like architecture with general formula ABX3 have been intensively studied in recent years due to a variety of applications including memory devices, energy conversion and gas storage. 1 , 2 , 3 In order to obtain a desirable material, many appropriate precursors are considered. Recently, widely studied type of precursor are metal-organic frameworks (MOFs), which contain both organic and inorganic components. 4,5,6,7,8,9,10,11 Generally, these compounds are constructed from metal ions/clusters (built from metal-oxygen or metal-nitrogen octahedra) coordinated by organic linkers (or bridging-ligands).12,13 The characteristic feature of such networks is presence of organic cations occupying the large void space. Each such a cavity contains a single organic cation, which establishes H-bonds with the metal-formate framework. Most efforts have been devoted to studies of metal formate frameworks with general formula [AmineH+][M(HCOO) 3], where M denotes a divalent metal ions. 14 , 15 , 16 ,

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Up to now, 11 different amines were

successfully applied in construction of such networks.18,19 The most intensively studied metal formates contain dimethylammonium (DMA+) cations.17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37 These compounds with metals M = Mn, Zn,

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Ni, Co, Fe (abbreviated as DMAM) crystallize in the trigonal space group 𝑅3̅𝑐, with the disordered organic cations. Each of the DMA+ cation is constantly hopping between the three equivalent positions located in the cages of the network.38,39 For these MOFs, the dynamics of the DMA+ cation and framework deformation play an essential role in driving the structural order-disorder phase transition.40,41 Depending on a metal center, the transition temperature is T0= 155−185 K.20,24,25,27,28,32,33 It was shown that these phase transitions coincide with the loss of the DMA+ cation three-fold symmetry. Strengthening of the hydrogen bonds at lower temperature often leads to ordering of the DMA+ cations, distortion of the framework and appearance of a long-range electric order.42,43 Below the first-order phase transition in low-temperature (LT) monoclinic Cc phase, where the hopping motion disappears, the DMA+ cations form regular checkerboard-like order with a non-zero spontaneous electric polarization indicating ferroelectric properties. 44 , 45 However, the polarization switching in electric hysteresis loop (proper ferroelectricity) was only observed for the perdeutero Co-formate compound37, which may suggest the improper ferroelectricity in these compounds. 46,47 Apart from the long-range electric order, DMAM analogues containing paramagnetic transition metal ions showed interesting magnetic properties below 36K.22,33, 48 , 49 , 50 Moreover, the experimental investigations (electron paramagnetic resonance (EPR)37, nuclear magnetic resonance (NMR)28, 51 , broadband dielectric spectroscopy (BDS)43,52 ) of the rotational reorientation between three equivalent sites within the zinc formate cage in the disordered phase provided the picture of the timescale of the DMA+ motion. The dielectric permittivity measurements revealed characteristic correlation time of the DMA+ dipole of 5.10-9 s at ambient conditions. This result remains in reasonably good agreement with the value of both the EPR correlation time of 2.10-9s and the NMR results 5.10-10 s.

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The phase transition and dynamic properties of these ferroic frameworks may be tuned by doping with both isovalent and aliovalent cations.23,53 In particular, doping leads to a shift of the phase transition temperature and the diffuseness of the phase transition.54 When doping is sufficiently large, the phase transition may no longer be observed. In addition, the doping results in new functionality of some of the studied multiferroic MOFs. For example, compounds doped with chromium or lanthanide ions were found to be promising luminescent materials.23 Recently, some of us reported a multifrequency EPR study of DMAZn framework doped with different amount of Cu2+ ions. 55 At low doping levels, we observed that the dynamic Jahn-Teller distortion of the CuO6 octahedra is coupled with the DMA+ cation motion providing additional local distortion of the framework. EPR spectra also revealed a distribution of the characteristic motional time of the DMA+ cation dynamics indicating the inhomogeneous distribution of the Cu2+ centers. At dopant concentration above 2 mol%, we also detected the magnetic exchange interaction between the copper centers indicating the tendency of these ions to accumulate into clusters. Despite these studies of doped DMAM frameworks, there are still many unanswered, although highly interesting, questions regarding the distribution of the dopants and their role on the structural phase transition and DMA+ cation motion. Herein we use several independent experimental techniques such as differential scanning calorimetry (DSC), BDS, X-ray diffraction, EPR and IR spectroscopy to study these questions in DMAZn framework doped with different amount of Cu2+ ions. 2. Experimental details Synthesis: CuCl2 (99.995%, Sigma-Aldrich), ZnCl2 (99%, Sigma-Aldrich), methanol (99.8 %, Sigma-Aldrich), 2.0 M solution of dimethylamine in methanol (Sigma-Aldrich) and formic

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acid (98%, Sigma-Aldrich). To obtain [(CH3)2NH2][Zn(HCOO)3] doped with 1 mol % of Cu2+, a solution containing 10 ml of methanol, 5 ml of 2.0 M solution of dimethylamine in methanol and 4 ml of HCOOH was placed at the bottom of glass tube (inner diameter of 9 mm). To this solution, 15 ml of a methanol solution containing 0.99 mmol of ZnCl2 and 0.01 mmol of Cu2+was gently added. The tubes were sealed and kept undisturbed. Crystals were harvested after 2 days. The [(CH3)2NH2][Zn(HCOO)3] compounds doped with 0.1, 0.5, 2, 3, 5 Cu2+mol% were obtained in the same way using the corresponding mixtures of metal salts. Relatively large single crystals of pure and doped with 1 and 3 Cu2+mol% were used for dielectric spectroscopy measurements. The content of metal elements was determined by the inductively coupled plasma method (ICP) (see Table S1), which was performed on an ARL 3410 ICP instrument. Crystal structure investigations: The single-crystal X-ray diffraction was collected on Xcalibur Atlas diffractometer equipped with Oxford Diffraction cooling system. CrysAlisPro was used for the data processing (CrysAlis PRO 1.171.38.43 (Rigaku OD, 2015)). Lattice parameters were calculated from the single-crystal X-ray diffraction by indexing at least 400 (in the case of pure DMAZn) and 500 (in the case of DMAZn0.95Cu0.05) Bragg peaks. The crystal structure of DMAZn and DMAZn0.95Cu0.05 at 165 K was refined in rhombohedral 𝑅3̅𝑐 symmetry, using SHELXL2014/7. 56 The results are shown in supplementary materials (see Table S2, S3, S4). It worth mentioning that the low-temperature phase was refined in the hexagonal R-3c setting for simplification; the detailed low-temperature structure will be presented in a future publication. DSC: Heat capacity was measured using Mettler Toledo DSC-1 calorimeter with high resolution of 0.4 µW. Nitrogen was used as a purging gas and the heating and cooling rate was 5 K/ min. The excess heat capacity associated with the phase transition was evaluated by

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subtraction from the data the baseline representing variation in the absence of the phase transitions. Dielectric properties: The dielectric properties of single crystals were measured as a function of frequency and temperature by means of a broadband impedance Novocontrol Alpha analyzer. The samples were investigated isothermally at frequencies from 1 Hz to 1 MHz. The measurement were taken with an increment of 1 K over the temperature range from 125 to 270 K. EPR: The continuous-wave EPR measurements were performed at the X-band microwave frequency (9.4 GHz) using a conventional Bruker ELEXSYS E580 EPR spectrometer. The strength and frequency of the modulating field were set to 6 G and 100 kHz, respectively. IR spectroscopy: IR spectra were measured with a Nicolet iS50 FTIR spectrometer for the samples in KBr pellets and Nujol mull in the 400-4000 and 500-50 cm-1, respectively. The spectral resolution of Raman and IR spectra was 2 cm-1. 3. Results and discussion 3.1. Room temperature vibrational studies In order to better understand the vibrational properties of the studied formates, all molecular vibrations should be divided into internal vibrations of HCOO- and DMA+ ions as well as the lattice vibrations. An isolated formate anion possesses C2v symmetry, and its fundamental internal vibrations consist of the C-H stretching (1), the symmetric (2) and antisymmetric (4) C-O stretching, the symmetric O-C-O bending (3), the C-H in-plane bending (5) and the C-H out-of-plane bending(6) 57 . A free DMA+ cation also has C2v symmetry and its 27 internal modes consist of: (i) symmetric (s(NH2)) and antisymmetric (as(NH2)) stretching, scissoring ((NH2)), rocking ((NH2)), wagging (ω(NH2)) and twisting (τ(NH2)) modes of the

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NH2group; (ii) symmetric (τs(CNC)) and antisymmetric (as(CNC)) stretching and bending ((CNC)) modes of the CNC group; (iii) symmetric (s(CH3)) and antisymmetric (as(CH3)) stretching, bending ((CH3)), rocking ((CH3)) and torsion (τ(CH3)) modes of the CH3 group33. The lattice modes may be divided into translational (T’) modes of M2+, HCOO- and DMA+ ions and librational (L) modes of HCOO- and DMA+ ions. The IR spectra of the studied compounds are presented in Figs. S1 and S2. IR wavenumbers for pure DMAZn and DMAZn doped with 5% of Cu2+ are listed in Table S5 together with the proposed assignments. The detailed description of the assignments of internal and lattice modes is omitted as it could be easily done using the literature data available for related formates with DMA+ cations.33,42,58 In the next part of the paper, we discuss however the influence of Cu-doping on the vibrational properties of DMAZn. Figures S1 and S2 as well as Table S5 show that doping with Cu2+ ions leads to weak changes in the shape and position of the IR bands. Since metal cations are connected via HCOOligands, some changes on doping are expected for bands arising from motions of these ligands. Indeed, doping with Cu2+ ions leads to slight shifts to lower wavenumbers of some internal modes bands (see Table S5 and Figs. S1, S2). For instance, doping with 5% of Cu2+ causes a shift of the strong IR band (3(HCOO-)) from 803 cm-1 to 801 cm-1. In contrast to this behavior, bands assigned to DMA+ vibrational motions do not exhibit any noticeable shifts. It is worth to add that DMACu crystalizes in a different symmetry than other members of DMAM family. Due to the Jahn-Teller effect, the crystal structure of DMACu is characterized by greater distortion, i.e., this compound crystallizes in a monoclinic structure whereas other divalent formates (including DMAZn) have rhombohedral structures.27,,59 The high similarity between the recorded spectra of studied by us samples within experimental accuracies (see Fig. S1) indicates that doping with Cu2+ cations up to 5 mol% has negligible

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effect on the vibrational properties. This behavior is consistent with the fact that a low doping level does not change the crystal structure. The spectra show larger differences in the region below 420 cm-1, where all bands can be attributed to the lattice modes. In particular, many modes exhibit upshift by 1-6 cm-1 for the DMAZn0.95Cu0.05 sample. This behavior can be attributed to the fact that wavenumbers of the translational modes depend significantly on the mass and size of ions building the structure. The atomic mass of Cu (63.5 u) is slightly smaller than the atomic mass of Zn (65.4 u). Moreover, the ionic radius of Cu2+ (0.87 Å) is also slightly smaller than the ionic radius of Zn2+ (0.88 Å). Therefore, translational modes of divalent metal ions should exhibit small shifts towards higher wavenumbers when zinc is replaced by copper. Shift of the 298 cm -1 band of DMAZn to 302 cm-1 for DMAZn0.95Cu0.05 is consistent with the expectation. However, downshift of the 246 cm-1 band on doping is not consistent with the expected behavior. Furthermore, upshifts can also be also observed for librational and translational modes of DMA+ and HCOO- ions (see Table S5). We suppose, therefore, that shift of the discussed bands on Cu2+ doping indicates that the lattice modes are strongly coupled and that the doped ions lead to some distortion of the metal-formate framework. 3.2. DSC DSC is a widely used technique in the field of material science because it allows easy detection of the phase transitions. However, this relatively fast method entails some inaccuracies. It is known that the excess entropy (∆S) at the phase transition depends significantly on the choice of the baseline. Currently there is a huge discrepancy of ∆S values for DMAM compounds in the literature, as summarized in Table 1, where ∆S varies from 0.9 up to 10 J mol-1 K-1. Such a large difference may be puzzling, especially knowing that change in entropy accompanies structural phase transition, with distinguished positions of the DMA+

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cation in the ordered and disordered phases. The entropy difference can be simply estimated from ∆S=Rln(N2/N1), where N1 and N2 are the numbers of distinguishable positions of the DMA+ cation. According to the X-ray diffraction data, in all the investigated structural analogs, the DMA+ cation occupies three disordered sites in the high-temperature phase (N2 = 3), and a complete ordering of these cations in the low-temperature phase (N1 =1) leading to ∆S = R ln(3) = 9.1 J mol−1 K−1. It should be pointed out, however, that the majority of the obtained values of entropy changes at T0 is smaller, which is usually explained by the more complex than order-disorder type mechanism of the investigated phase transition. Recently, the importance of framework deformation on mechanism of order-disorder phase transition in DMA metal formates was suggested.16,43,55,60 To give some input to this called “chicken or eggs” dispute41, the series of Cu-doped DMAZn compounds were thermally measured. Table 1. Comparison of phase transition properties of different DMAM compounds.a Compound DMA Mn(HCOO)3

DMA Co(HCOO)3 DMA Mg(HCOO)3

DMA Zn(HCOO)3 DMA FeFe(HCOO)3 DMA NaFe(HCOO)3 a

T0[K] 180ex , 190en 183ex , 190en 183 182ex , 190en 149ex , 159en 258ex , 263en 262ex, 264en 259ex , 267en 259ex , 265en 156 156 152ex , 155en 167ex , 171en

Δ S [J mol-1 K-1] 8.8 - 9.4 [20] 8.9 - 9.3 [21] 0.9 [22] 4.7 [23] 3.4 [23] 4.6 [24] 11.3 [25] 10 ±1 [25] 5.9 [23] 1.1 [27] 1.1 [28] 2.44 [29] 0.9 [30]

Superscripts ex and en denote the exothermic and endothermic process, respectively.

The DSC thermographs of pure DMAZn compound show sharp heat anomaly at approximately 167 K upon heating and at 156 K upon cooling (cf. Figure S3). The shape of the anomaly, relatively large thermal hysteresis of 8 K and a sharp peak indicate a reversible first-order phase transition, which is in good agreement with previously reported results.27,28 The estimated value of ∆S of the studied compounds are listed in Table S6. The obtained ∆S

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value (4.25 J mol-1 K-1) for pure DMAZn is higher compared to the previously reported value for this compound,27,28 but smaller than the one expected from the order-disorder relation. The properties of the phase transitions of DMAZn:Cu2+ changes with increasing concentration of Cu2+ ions. The changes in the heat capacity and entropy related to the structural phase transition are presented in Fig. 1. The excess specific heat associated with the order-disorder phase transition becomes much broader and strongly asymmetric, leading to the decrease of ∆S (Fig. 2a). Moreover, the first noticeable difference caused by Cu2+ doping is the lowering of the phase transition temperature (Fig. 2b). The smearing of the anomaly with increasing Cu2+ concentration indicates the diffusive character of the phase transition. Such behavior was also noticed for other hybrid compounds, for which a shift of the phase transition, broadening of thermal anomalies and a decrease of the transition entropy also increased with rising concentration of the dopant.23,54,60 The observed decrease of the phase transition temperature and entropy can be explained by taking into account that pure DMACu compound does not exhibit structural phase transition, due to the Jahn-Teller distortion of the framework.16,60 Thus, the doping of DMAZn with Cu2+ causes significant local structural deformation, which impedes the DMA+ cation motion. With the increase of copper content, a smaller fraction of the crystal remains unperturbed leading to the smearing of the anomalies and decrease of the phase transition temperature and entropy.

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heating a

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Figure 1. (a) The change in heat capacity and entropy related to the phase transition in Cu2+ doped DMAZn measured in (a) heating and (b) cooling modes.

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Figure 2. (a) The entropy change at phase transition temperature versus Cu2+ content is presented. The solid curve in (a) is guide for eyes.(b) The phase transition temperature dependence T0 vs Cu2+ content during heating and cooling process.

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3.3. X-ray diffraction Figure 3 illustrates the thermally induced changes in lattice parameters for undoped DMAZn and doped DMAZn0.95Cu0.05 samples. As it can be noticed in Table S7 and S8 the small Cu2+ substitution for Zn2+ results in a decrease of all unit cell parameters (rhombohedral𝑅3̅𝑐, hexagonal setting). The unit cell volume at 260 K for the undoped sample is equal to ~1294 Å 3

whereas for the DMAZn0.95Cu0.05 it equals to ~1287Å3. Cu and Zn are two d-block neighbors

that possess almost the same scattering factors for the X-rays, thus it is impossible to refine the real concentration of copper substituent in the structure. Additionally, both Cu2+ and Zn2+ possess almost identical ionic radii in the octahedral coordination (0.87 and 0.88 Å, respectively). 61 Cu and Zn differ, however, with the covalent radii (1.28 Å for Cu and 1.33Å for Zn 62 or 1.12 for Cu and 1.18 for Zn 63) and, that is even more important, in Jahn-Teller activity, which may be responsible for the observed differences in the size of the unit cells. The chemical substitution influences the character and the temperature of the structural phase transition from 𝑅3̅𝑐 phase to the LT structure. In agreement with DSC measurements, the T0 shifts towards lower temperatures for DMAZn0.95Cu0.05 sample. In addition, the structure distortion associated with the symmetry lowering is remarkably lower in Cu-modified DMAZn formate. This is mostly demonstrated by the temperature changes of the c-lattice parameter, which experiences a sharp increase at T0 in pure crystals and has almost continuous character in Cu-modified sample. Additionally, the twinning of the single-crystals that appears below the phase transitions, as a result of the symmetry decrease, results in considerable different diffraction picture in both compounds. In DMAZn the domain structure results in split diffraction patterns, demonstrating large structural distortion, whereas in DMAZn0.95Cu0.05 the splitting appears below 140K. Figure S4 the reciprocal space reconstructions for both crystals taken at 200, 160 and 140K, whereas Fig S5 shows the

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reciprocal space reconstructions for DMAZn0.95Cu0.05 at selected temperatures together with the temperature evolution of the intensity profile of 0 -5 2 Bragg peak.

Figure 3. Thermal evolution of lattice parameters for pure and Cu-doped DMAZn, (the constrained unit cell from the high-temperature phase; hexagonal setting with a=b, c and α=90, β=90, =120) The changes in the character of the phase transition must be directly related to the coordination preferences of the Cu2+ ions. Due to the Jahn-Teller effect, which is very common in six-coordinate copper(II) complexes, the Cu2+ ions are not very keen on adopting the high-symmetry sites.

64

Cu-formates usually adopt layered structures which allow for

significant elongation of Cu – O axial bonds 65 or perovskite-like with distinctly distorted octahedral coordination.59 The structure of DMACu is monoclinic, I2/c, with equatorial Cu-O bonds of 1.969 - 1.971 Å and the axial Cu-O bonds of 2.492 Å. In the rhombohedral 𝑅3̅𝑐 lattice Zn2+ ions are located at -3. (S6) positions in the centers of rhombohedraly distorted

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octahedrons, having the same Zn-O distances (2.109 Å at 165K, see Table S3). Simultaneously with the copper substitution for zinc, the site hindrance is incorporated into the structure. The amount of the dopant is too low, however, to induce the long-range symmetry changes, but on the local scale, the Cu2+ ions possibly adopt the off-centered positions. Larger anisotropic displacement parameters U (calculated at 165 K) observed in copper modified crystals at Zn/Cu sites(U11=U22: 0.01165, U33= 0.01218) compared to fully occupied by Zn positions in pure DMAZn-formate (U11=U22: 0.00861, U33= 0.00984) seem to confirm this hypothesis. Additionally, the off-center displacements of copper ions may accommodate the internal strain that develops at temperatures close to the T0 delaying the symmetry breaking (lowering the T0) and decreasing the magnitude of the distortion. 3.4. EPR We further performed continuous-wave EPR measurements to probe the distribution and local environment of Jahn-Teller active Cu2+ dopants. The room temperature EPR spectra of DMAZn doped with different amount of paramagnetic Cu2+ ions(electron spin S = ½) are presented in Figure 4.The spectra consist of the typical axially symmetric powder pattern of Cu2+ ions superimposed with an additional broad line. As discussed in our previous study53, these two signals originate from the inhomogeneous Cu2+ ion distribution in the crystal. Regions with a low copper concentration provide weak framework distortion, which results in a relatively unhindered hopping motion of the DMA+ cations. Consequently this motion via the H-bonds constantly deforms the neighboring CuO6 octahedra. This results in a partial averaging of the Cu2+g-tensor anisotropy leading to the broad EPR line.55 In contrast, regions with a high copper concentration provide strong Jahn-Teller distortion of the framework, which results in the significantly hindered DMA+ cation motion. As a result, the CuO6octahedra experience slower dynamics providing anisotropic axially symmetric powder pattern. With increasing dopant concentration, the hyperfine structure of the axially

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symmetric signal disappears due to the increased dipolar and exchange couplings between the Cu2+ ions. The EPR spectra obtained in the ordered phase at 120 K are also presented in Figure 4. The spectrum at the lowest doping level of 0.1 mol% solely consists of the anisotropic axially symmetric powder pattern, as the ceased DMA+ cation motion no longer influences the CuO6 octahedra. However, as the copper concentration increases, another broad line appears indicated by the arrow in Figure 4. The intensity of this signal increases with increasing doping level. The origin of this line is the exchange coupled Cu2+ ions from the crystal regions with a very high (close to 100 %) copper concentration. 66 This observation also indicates inhomogeneous copper distribution within the DMAZn structure.53

DMAZn0.999Cu0.001 DMAZn0.99Cu0.01 DMAZn0.98Cu0.02

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Magnetic field (mT)

400

DMAZn0.97Cu0.03 DMAZn0.95Cu0.05

240

280

320

120 K

360

400

Magnetic field (mT)

Figure 4. X-band continuous-wave EPR spectra of DMAZn doped with different Cu2+ concentration obtained at (left) 292 and (right) 120 K. The arrow indicates EPR signal from exchange coupled Cu2+ ions. 3.5. Dielectric studies

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To probe the dynamics of pure and Cu2+-doped DMAZn framework on an extensive time scale, we performed broadband dielectric spectroscopy experiments of a single crystal sample in a 1Hz to 1MHz frequency range. The temperature dependences of the complex dielectric permittivity 𝜀 ∗ = 𝜀 ′ − 𝑖𝜀 ′′ of the investigated samples are presented in Figure 5. For pure DMAZn a discontinuous anomalous decrease of both ε’ and ε” can be observed at T0. This indicates the first-order structural phase transition which is in a good agreement with other studies51. With increasing content of Cu2+ ions the phase transition temperature shifts to lower temperatures and associated anomaly of 𝜀 ∗ becomes more smeared, suggesting change in the phase transition character. Above the phase transition temperature, the complex dielectric permittivity shows characteristic dipolar relaxation process in a broad frequency and temperature range. It is worth noting that the values of ε’ decreases with the increasing number of dopant. This indicates that small amount of Cu2+ ions cause local structure deformation, which pertube polarizability of the investigated structures. A close inspection of the complex dielectric permittivity data in the frequency domain reveals that in the direction perpendicular to the (012) plane, above phase transition temperature, a single dipolar relaxation process appears (Fig. 6a).

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Figure 5. Temperature dependence of dielectric permittivity (upper panels) and dielectric loss (lower panels) measured in the direction perpendicular to the (012) plane for selected frequencies for DMAZn (left), DMAZn0.99Cu0.01 (middle) and DMAZn0.97Cu0.03 (right). The arrows indicates the changes of the probing frequency changes.

Dielectric loss ''

10

DMAZn

218 K

a

DMA_Zn ; Ea=0.284 eV

b

DMA_Zn_1Cu ; Ea=0.279 eV

1

164 K

-4.5

0.1 10 DMAZn

0.99

-5.0

204 K

Cu0.01

1

-5.5

158 K

0.1 10

-4.0

DMA_Zn_3Cu ; Ea=0.274 eV

log (max (s))

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-6.0 DMAZn0.97Cu0.03

206 K

1

-6.5

0.1 102

140 K 3

10

4

10

105

-7.0 4.5 5.0 5.5 6.0 6.5 7.0

106

Frequency (Hz)

1000/T (K-1)

Figure 6. (a) Frequency dependence of imaginary part of the dielectric permittivity ε’’(ω) for investigated DMAZn:Cu single crystal samples. In all the investigated samples characteristic dipolar relaxation peak shifts to higher frequencies with increasing temperature.(b) Dependence of the mean relaxation time of DMA+ cation motion as a function of inverse temperature obtained for three studied single crystals. The linear fits indicate Arrhenius processes. It was observed that the dielectric response of all the investigated samples follows the anomalous relaxation mechanism represented by low- (𝑚) and high-frequency (𝑛 − 1) powerlaw dependence of the imaginary part of the dielectric permittivity on frequency, i.e.: 𝑚

𝜀 ′′ (𝜔) ∝ (𝜔/𝜔𝑝 ) for 𝜔 < 𝜔𝑝 , 𝜀 ′′ (𝜔) ∝ (𝜔/𝜔𝑝 )

𝑛−1

for 𝜔 > 𝜔𝑝 ,

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where𝜔𝑝 denotes the loss peak frequency and 0 < 𝑚, 𝑛 < 1. Moreover, it was found that regardless of the Cu content in the studied samples the low and high-frequency power-law exponents satisfy relation 𝑚 ≥ 1 − 𝑛. It is known that such relaxation data can be interpreted within relaxation scenario leading to the well-known Havriliak-Negami (HN) relaxation function67,68: ∗ (𝜔) 𝜑𝐻𝑁 =1−

1 𝛼 𝛾

[1+(𝑖𝜔/𝜔𝑝 ) ]

,

0 < 𝛼, 𝛾 < 1.

(1)

The above equation, together with the boundary cases 𝛼 < 1, 𝛾 = 1 (Cole-Cole (CC) function) and 𝛼 = 1, 𝛾 < 1, (Cole-Davidson (CD) function) can be successfully used to fit the typical, frequency-domain power-law relaxation data (see Fig. 7a). The HN and CC formulas satisfy low and high-frequency power-laws with 𝑚 = 𝛼and 1 − 𝑛 = 𝛼𝛾. The CD function exhibits the high-frequency power-law only. To determine the parameters of the relaxation dynamics of the observed dipolar process, the inverse temperature dependence of the mean dielectric relaxation time τ was analyzed as a function of the inverse of temperature (see Fig. 6b). This relaxation map reflects the dynamic properties of the investigated structures. For all the three investigated single crystals samples the τ(T-1) dependence exhibits a clear linear behavior obeying the classical Arrhenius law. The linear fit to the experimental data for pure DMAZn provided activation energy of Ea= 284(5) meV being in a good agreement with rotational movement of DMA ion in analog compounds.25,38,41 The activation energy of the Cu-doped samples slightly decreases with increasing dopant concentration. Due to low concentration of Cu2+ dopant, the activation energy reflects dynamics of DMA+ cations located near Zn2+ sites. Decrease of Ea on doping indicates that although Jahn-Teller deformation hinders motions of DMA+ cations located near Cu2+ sites, the local framework deformation causes slightly easier rotation of the DMA+

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cations, which are distant from the Cu2+centers.This indicates that small amount of Cu2+ ions significantly reduces polarizability of the investigated structures, probably due to Cu-induced disorder related with the off-center displacements of copper ions that leads to decrease of the distortion (see discussion of X-ray diffraction data). It is worth noting that the frequency-domain relaxation patterns leading to the relaxation functions mentioned above may be derived from the correlated cluster scenario.69,70,71 In this approach it is assumed that relaxation behavior of an investigated system may be described in terms of a random variable 𝛽̃, which is interpreted as the effective relaxation rate of a system. Empirically detected non-exponential relaxation in the time-domain results from averaging of the classical Debye relaxation response over distribution of the random, effective relaxation rate 𝛽̃ . The explicit form of the effective relaxation rate and the corresponding density function determines the type of measured relaxation response. Moreover, within correlatedclusters scenario, the relaxation pattern exhibited by the whole system of a size 𝑁 is assumed to be

influenced by the statistical properties of individual microscopic relaxation

𝜐𝑁 contributions 𝛽𝑖𝑁 's, so that 𝛽̃ = ∑𝑖=1 𝛽𝑖𝑁 , where 𝜐𝑁 denotes random number of microscopic

relaxation contributions to the total (effective) relaxation rate. It is worth mentioning, that relaxation scenarios based on correlated-cluster approach require the appearance of mutual interactions of microscopic relaxation contributions being in a various charge states leading, in consequence, to formation of “pure” dipoles or at least dipole-like objects. In general, within the correlated-cluster scheme it is assumed that there is a random number 𝐾𝑁 of ‘active’ elements (dipoles) essentially contributing to the relaxation rate of the system. The ith ‘active’ dipole is surrounded by random number 𝑁𝑖 − 1 of ‘inactive’ neighbours forming together a randomly-sized cluster. The correlated-clusters relaxation scenario assumes mutual dipole-dipole interactions. Therefore, not only single dipole relaxation gives input to the

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effective relaxation rate of a system but also a collective dipole-dipole effect is considered. As a result of correlation of neighboring dipoles, a random number of cooperative regions (superclusters) of sizes 𝑀1 , 𝑀2 … build up from the ‘active’ dipoles may be formed. The effective relaxation rate is a sum of all 𝐿𝑁 super-cluster contributions. Similarly, the particular supercluster's relaxation rate results from summing up the contributions of all dipoles present in this region (for details see64,65,66). Therefore, the random total relaxation rate β̃N reads 𝛽̃𝑁 = 𝑀

𝑗 𝑁 ∑𝐿𝑗=1 ∑𝑖=1 𝛽𝑖𝑗𝑁 , where 𝛽𝑖𝑗𝑁 is the contribution of the 𝑖 −th dipole of the 𝑗 −th super-cluster. If

the number 𝑁 is lare one can replace 𝛽̃𝑁 with its limit in distribution 𝛽̃ as 𝑁 → ∞. The distributions of quantities 𝑁𝑖 's, 𝑀𝑗 's, and 𝛽𝑖𝑗𝑁 's determine the properties of limiting random variable 𝛽̃, representing the whole relaxing system and, in a consequence, the behavior of the ̃

∗ (𝜔) relaxation function 𝜙(𝑡) = 〈𝑒 −𝛽𝑡 〉. Note that, the frequency-domain response 𝜑𝐻𝑁 can be

related to the time-domain relaxation function ΦHN (t) by the one-sided Fourier transform62: ∞

∗ (𝜔) 𝜑𝐻𝑁 = ∫0 (−

𝑑Φ𝐻𝑁 (𝑡) 𝑑𝑡

) 𝑑𝑡. It follows from limit theorems of probability theory that the

necessary and sufficient conditions for the existence of the HN relaxation rate 𝛽̃𝐻𝑁 are heavytailed (broad) distributions of super-cluster sizes 𝑀𝑗 , cluster sizes 𝑁𝑖 and ‘active’ dipole relaxation rates 𝛽𝑖𝑗𝑁 70707171). The presence of a single peak in the measured dielectric response of the DMAZn and DMAZn:Cu samples indicates that these frameworks exhibit dielectric properties characteristic for dipolar system. It is highly likely that electric dipoles in these samples correspond to the DMA+ molecules.41 However, the reasoning presented above and HN behavior of the frequency response of measured samples indicates substantial interaction between these dipoles spanning clusters or mesoscopic regions (superclusters). Superclusters formation may indicate long-range interactions between DMA+ cations. Note that a similar clustering behavior in DMAZn and [(CH2)3NH2][M(HCOO)3] (M = Zn, Mg) frameworks was

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also observed by NMR spectroscopy.52,72 As recently demonstrated37, such clusters do not correspond to the polar nanoregions observed in relaxor ferroelectrics.

DMAZn 10

a

195

1.00

b

180

0.95

165

0.90

Dielectric loss ''

150

DMAZn0.99Cu0.01

84 80

1

DMAZn0.97Cu0.03

76 48



1

Dielectric permittivity '

0.85

DMAZn DMAZn0.99Cu0.01 DMAZn0.97Cu0.03

46

1

0.80

1.0



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0.8

44 104

105

Frequency (Hz)

42 106

160

170

180

190

200

0.6

Temperature (K)

Figure 7. (a) Frequency dependence of the complex dielectric permittivity of DMAZn:Cu at 180K. The solid curves in (a) represent fits of the experimental data by the HN function.(b)Temperature dependence of the HN power-law exponents characteristic for relaxation response of DMAZn:Cu samples.

In Figure 7b temperature dependence of the power-law exponents 𝛼, 𝛾 in relaxation response of DMAZn:Cu samples is shown. It is clear from the plot that no significant changes in the values of parameters 𝛼, 𝛾 on temperature are observed in case of the undoped sample, whereas for both the doped samples the increase of the value of 𝛼 and decrease of the value of 𝛾 parameter with increasing temperature were detected. It can be observed that for undoped DMAZn the values of the cluster sizes and single dipoles relaxation rate distribution tail exponent 𝛼are close to 1, which indicates clusters of similar sizes formation in the material and the very similar relaxation behavior of each relaxation contribution actively responding to

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the applied electric field changes. The value of supercluster sizes distribution tail exponent 𝛾 within the margin of estimation error is equal to approximately 0.86, which suggests the very small supercluster sizes spread. In case of the undoped material both the microscopic and mesoscopic structure appears not to be prone to temperature changes. Doping leads to structural changes in the sense that in DMAZn0.99Cu0.01 and DMAZn0.97Cu0.03 clusters sizes are more spread comparing to the undoped DMAZn, which is highly likely related to inhomogeneous distribution of copper in DMAZn as revealed by EPR spectroscopy.55 It is worth noting, however, that in case of 1% Cu2+ content the cluster sizes distribution as well as the relaxation rate behavior above 170K is very similar to the undoped sample, whereas 3% Cu2+ content leads to the more significant spread of cluster sizes and broader single dipoles relaxation rates distribution. Analysis the temperature dependence of 𝛾 parameter allows to conclude that both the doped samples exhibit similar behavior as long as the mesoscopic regions distribution is concerned. The superclusters distribution becomes heavier with increasing temperature (larger superclusters sizes spread is expected).

Conclusions In this work a comprehensive set of experimental techniques was used to study the impact of Zn substitution by Cu doping on the order-disorder phase transition in a model dense metal-organic framework dimethylammonium zinc formate [(CH3)2NH2][Zn(HCOO)3] (DMAZn). In particular, we have examined the role of the Jahn-Teller effect of Cu2+ ions which lead to a local framework distortion and the impacts the structural dynamics. The single crystal X-ray diffraction revealed that the small Cu2+ substitution for Zn2+ does not change the symmetry at room temperature (rhombohedral𝑅3̅𝑐) and results solely in the observed decrease of all unit cell parameters. This result corroborates with the IR measurements indicating that with the experimental accuracies doping with Cu2+cations up to

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5 mol% possesses a negligible effect on the vibrational properties. Moreover, the EPR measurements revealed the inhomogeneous copper distribution within the DMAZn structure. The DSC measurements of DMAZn:Cu2+ indicates that the phase transition changes with increasing concentration of Cu2+ ions. The Cu2+ doping leads to the lowering of the phase transition temperature and decrease of entropy changes. The revealed smearing of the anomaly with increasing Cu2+ concentration indicates diffusive character of the phase transition. The observed changes can be explained by taking into account the Jahn-Teller distortion of the framework. The doping of DMAZn with Cu2+ causes significant local structural deformation with stronger N-H…O-Cu bonding, which impedes the DMA+ cation motion. With the increase of copper content, a smaller fraction of the crystal remains unperturbed, leading to the smearing of the anomalies and decrease of the phase transition temperature and entropy. The dynamics of the DMA+ cations was also investigated using the broadband dielectric spectroscopy for single crystals of DMAZn:Cu2+ . We observed a dipolar relaxation process in the HT (disordered) phase, which is consistent with the DMA+ cation ordering in DMA-metal formates. The Arrhenius plot showed that activation energy of the Cu-doped samples decreases from 0.284±0.002 eV to 0.274±0.002 eV with increasing dopant concentration from 0 to 3%. Such a behavior indicates that local framework deformation causes slightly easier rotation of the DMA+cations, which are distant from the Cu2+ centers. Moreover, detailed dielectric permittivity measurements in frequency domain revealed that interactions between the electric dipoles of DMA+ leads either to the formation of clusters or mesoscopic regions (superclusters). In case of undoped DMAZn crystal these clusters are of similar sizes and the very similar relaxation behavior of each relaxation contribution actively responding to the applied electric field changes expected to be, whereas the superclusters sizes are spread.

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Doping results in local structural changes and leads to the clusters sizes variation comparing to the undoped DMAZn, which is highly likely related to inhomogeneous distribution of copper in DMAZn as revealed by EPR spectroscopy.

Supporting Information Details of structural results, IR spectra and DSC measurements data.

Acknowledgements The authors are deeply grateful for financial support by the National Science Centre within the framework of the Opus13 project (Grant No. DEC-2017/25/B/ST3/02321).

References [1]Kostopoulou, A.; Kymakis, E.; Stratakis, E. Perovskite nanostructures for photovoltaic and energy storage devices, J. Mat. Chem. A, 2018, 6, 9765-9798. [2] Masoomi, M. Y.; Morsali, A. Applications of metal-organic coordination polymers as precursors for preparation of nano-materials, Coord. Chem. Rev., 2012, 256, 2921−2943. [3] Kitagawa, S.; Kitaura, R.; Noro, S-I. Functional Porous Coordination Polymers, Angew. Chem., 2004, 43, 2334-2375. [4] Cheetham, A.K. ; Rao, C. N. R. There’s Room in the Middle,Science, 2007, 318, 58–59. [5] Oar-Arteta, L.; Wezendonk, T.; Sun, X.; Kapteijn, F.; Gascon, J. Metal organic frameworks as precursors for the manufacture of advanced catalytic materials, Mater. Chem. Front., 2017, 1, 1709−1745. [6] Wang, Z.; Hu, K.; Gao, S.; Kobayashi, H. Formate-Based Magnetic Metal–Organic Frameworks Templated by Protonated Amines, Adv. Mat., 2010, 22, 1526-1533.

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[7] Bosch, M.; Yuan, S.; Rutledge, W.; Zhou, H.-C. Stepwise synthesis of metal-organic frameworks, Acc. Chem. Res., 2017, 50, 857−865. [ 8 ] Shang, R.; Chen, S; Wang, S. M.; Gao, S. in Metal-Organic Framework Materials; MacGilliveay, R. L., Ed.; Lukehart C. M., Ed.; John Wiley & Sons Ltd.,2014, 221-238. [9] Tang, J.; Yamauchi, Y. MOF morphologies in control, Nat. Chem.,2016, 8, 638−639. [ 10 ] Li, W.; Thirumurugan, A.; Barton, P. T.; Lin, Z.; Henke, S.; Yeung, H. H. M.; Wharmby, M. T. ; Bithell, E. G.; Howard, C. J.; Cheetham, A. K. Mechanical Tunability Via Hydrogen Bonding In Metal–Organic Frameworks With The Perovskite Architecture, J. Am. Chem. Soc., 2014, 136, 7801-7804. [11] Mączka, M.; Gagor, A.; Ptak, M.; Paraguassu, W.; da Silva, T. A.; Sieradzki, A.; Pikul, A. Phase Transitions and Coexistence of Magnetic and Electric Orders in the Methylhydrazinium Metal Formate Frameworks, Chem. Mater.,2017, 29, 2264–2275. [12] Lu, W.; Wei, Z.; Gu, Z.-Y.; Liu, T.-F.; Park, J.; Park, J.; Tian, J.; Zhang, M.; Zhang, Q.;Gentle III, T.; Bosch, M.; Zhou, H.-C.Tuning the structure and function of metal–organic frameworks via linker design, Chem. Soc. Rev., 2014, 43, 5561-5593. [ 13 ]

Xu, W.-J.; Du, Z.-Y.; Zhang, W.-X.; Chen,

X.-M.Structural phase transitions in

perovskite compounds based on diatomic or multiatomic bridges, Cryst. Eng. Comm.,2016, 18, 7915-7928. [14] Šimėnas, M. ; Kultaeva, A.; Balčiūnas, S.; Trzebiatowska, M.; Klose, D.; Jeschke, G.; Mączka, M.; Banys, J.; Poppl, A. Single Crystal Electron Paramagnetic Resonance of Dimethylammonium and Ammonium Hybrid Formate Frameworks: Influence of External Electric Field, J. Phys. Chem. C, 2017, 121, 16533-16540.

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[15] Šimėnas, M.; Macalik, L.; Aidas, K.; Kalendra, V.; Klose, D.; Jeschke, G.; Mączka, M.; Volkel, G.; Banys, J.; Poppl, A. Pulse Epr And Endor Study Of Manganese Doped [(CH3)2NH2][Zn(HCOO)3] Hybrid Perovskite Framework, J. Phys. Chem. C, 2017, 121, 27225-27232. [ 16 ] Ptak, M.; Svane, K.L.; Walsh, A.; Paraguassu, W. Stability and flexibility of heterometallic formate perovskites with the dimethylammonium cation: pressure-induced phase transitions , Phys. Chem. Chem. Phys., 2019, 21, 4200-4208. [17] Šimėnas, M.; Ptak, M.; Khan, A. H.; Dagys, L.; Balevicius, V.; Bertmer M.; Volkel, G.; Mączka, M.; Poppl, A.; Banys, J. Spectroscopic Study Of [(CH 3)2NH2][Zn(HCOO)3] Hybrid Perovskite Containing Different Nitrogen Isotopes, J. Phys. Chem. C, 2018, 122, 10284-10292. [18] Shi, C.; Han, X.-B.; Zhang, W. Structural phase transition-associated dielectric transition and ferroelectricity in coordination compounds, Coord. Chem.Rev., 2019, 378, 561-576. [ 19 ] Mączka, M.; Janczak, J.; Trzebiatowska, M.;

Sieradzki, A.; Pawlus, S.; Pikul, A.

Synthesis and temperature-dependent studies of a perovskite-like manganese formate framework templated with protonated acetamidine,Dalt. Trans.,2017, 46, 8476-8485. [20] Sanchez-Andujar, M.; Gomez-Aguirre, L. C.; PatoDoldan, B.; Yanez-Vilar, S.; Artiaga, R.; Llamas-Saiz, A. L.; Manna, R. S.; Schnelle, F.; Lang, M.; Ritter, F.; Haghighirad, A. A.; Senaris-Rodriguez, M. A. First-order structural transition in the multiferroicperovskitelike formate [(CH3)2NH2][Mn(HCOO)3], Cryst. Eng. Comm.,2014, 16, 3558-3566. [21] Zhang, Z.; Tang, H.; Cheng, D.; Zhang, J.; Chen, Y.; Shen, X.; Yu, H. Strain coupling and dynamic relaxation in multiferroic metal-organic framework [(CH3)2NH2][Mn(HCOO)3] with perovskite structure, Res. Phys. , 2019, 12, 2183-2188.

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[22] Jain, P.; Ramachandran, V.; Clark, R. J.; Zhou, H. D.; Toby, B. H.; Dalal, N. S.; Kroto, H. W.; Cheetham, A. K. MultiferroicBehavior Associated with an Order-Disorder Hydrogen Bonding Transition in Metal-Organic Frameworks (MOFs) with the Perovskite ABX3 Architecture, J. Am. Chem. Soc, 2009, 131, 13625-13627. [ 23 ] Mączka, M.; Sieradzki, A.; Bondzior, B.; Dereń, P.; Hanuza, J.; Hermanowicz, K. Effect of aliovalent doping on properties of perovskite-like multiferroic formates, J. Mat. Chem. C, 2015, 3, 9337-9345. [24] Pato-Doldan, B.; Sanchez-Andjuar, M.; Gomez-Aguirre, L. C.; Yanez-Vilar, S.; LopezBezeiro, J.; Gracia-Fernandez, C.; Haghighirad, A. A.; Ritter, F.; Castro-Garcia, S.; SenarisRodriguez M. A. Near room temperature dielectric transition in the perovskiteformate framework [(CH3)2NH2][Mg(HCOO)3], Phys. Chem. Chem. Phys., 2012, 14, 8498-8501. [25] Szafranski, M.; Wei, W. –J.; Wang, Z.-M.; Li, W.; Katrusiak, A.

Research Update:

Tricritical point and large caloric effect in a hybrid organic-inorganic perovskite, APL Materials, 2018, 6, 100701. [26] Asaji, T.; Yoshitake, S.; Ito, Y.; Fujimori, H.Phase transition and cationic motion in the perovskiteformate framework [(CH3)2NH2][Mg(HCOO)3], J. Mol. Struct., 2014, 1076, 719723. [27] Jain, P.; Dalal, N. S.; Toby, B. H.; Kroto, H. W.; Cheetham, A.K. Inorganic-Organic Framework with the Perovskite Architecture, J. Am. Chem. Soc.,2008, 130, 10450–10451. [28] Besara, T.; Jain, P.; Dalal, N. S.; Kuhns, P. L.; Reyes, A. P.; Kroto, H. W.; Cheetham, A. K.; Mechanism of the order-disorder phase transition, and glassy behavior in the metal-

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organic framework [(CH3)2NH2]Zn(HCOO)3, Proc. Nat. Academy Sci., 2011, 108, 68286832. [29] Ciupa, A.; Mączka, M.; Gągor, A.; Sieradzki, A.; Trzmiel, J.; Pikul, A.; Ptak, M. Temperature-dependent studies of [(CH3)2NH2][FeIIIMII(HCOO)6] frameworks (MII = Fe and Mg): structural, magnetic, dielectric and phonon properties, Dalton Trans., 2015, 44, 8846– 8854. [30] Mączka, M.; Pietraszko, A.; Macalik, L.; Sieradzki, A.; Trzmiel, J.; Pikul, A. Synthesis and order–disorder transition in a novel metal formate framework of [(CH3)2NH2]Na0.5Fe0.5(HCOO)3],Dalton Trans., 2014, 43, 17075-17084. [ 31 ] Ptak, M.;

Gągor, A.; Sieradzki, A.;

Bondzior, B.; Dereń, P.;

Ciupa, A.;

Trzebiatowska, M.; Mączka, M. The Effect Of K +Cations On The Phase Transitions, And Structural, Dielectric And Luminescence Properties Of [Cat][K 0.5Cr0.5(HCOO)3], Where Cat Is Protonated Dimethylamine Or Ethylamine, Phys. Chem. Chem. Phys., 2017, 19, 12156-12166. [ 32 ] Duncan,H. D.; Dove, M. T.; Keen, D. A.; Phillips, A. E.Local Structure Of The Metal–Organic Perovskite dimethylammonium Manganese(II) Formate, Dalton Trans., 2016, 45, 4380-4391. [33] Mączka, M.; Gągor, A.; Macalik, B.; Pikul, A.; Ptak, M.; Hanuza, J. Order–Disorder Transition and Weak Ferromagnetism in the Perovskite Metal Formate Frameworks of [(CH3)2NH2][M(HCOO)3] and [(CH3)2ND2][M(HCOO)3](M= Ni, Mn),Inorg. Chem.,2013, 53, 457-467. [34] Abhyankar, N.; Bertaina, S.; Dalal, N. S. On Mn2+ EPR probing of the ferroelectric transition and absence of magnetoelectric coupling in dimethylammonium manganese

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formate (CH3)2NH2Mn(HCOO)3, a metal-organic complex with the Pb-free perovskite framework,J. Phys. Chem. C, 2015, 119, 28143-28147. [35] Šimėnas, M.; Balčiūnas, S.; Mączka, M.; Banys, J.; Tornau, E. E. Structural Phase Transition In Perovskite Metal–Formate Frameworks: A Potts-Type Model With Dipolar Interactions, Phys. Chem. Chem. Phys.,2016, 18, 18528-18535. [36] Bertaina, S.; Abhyankar, N.; Orio, M.; Dalal, N. S. Measuring Motional Dynamics Of [(CH3)2NH2]+

In

The

Perovskite-Like

Metal–Organic

Framework

[(CH3)2NH2][Zn(HCOO)3]: The Value Of Low-Frequency Electron Paramagnetic Resonance, J. Phys. Chem. C,2018, 122, 16431–16436. [37] Fu, D. –W.; Zhang, W.; Cai, H.-L.; Zhang, Y.; Ge, J.-Z.; Xiong, R.-G.; Huang S. D.; Nakamura,

T.

A

multiferroicperdeutero

metal-organic

Framework

[(CD3)2ND2][Co(DCOO)3], Angew. Chem., Int. Ed., 2011, 50, 11947–11951. [38] Li, W.; Wang, Z.; Deschler, F.; Gao, S.; Friend, R.H.; Cheetham, A. K. Chemically diverse and multifunctional hybrid organic–inorganic perovskites, Nat. Rev. Mater.,2017, 2, 16099. [ 39 ] Asadi, K.;

van der Veen, M. A. Ferroelectricity in Metal-Organic Frameworks:

Characterization and Mechanisms, Eur. J. Inorg. Chem., 2016, 2016, 4332–4344. [40] Mączka, M.; Ptak, M.; Macalik, L. Infrared and Raman studies of phase transitions in metal-organic frameworks of [(CH3)2NH2][M(HCOO)3] with M=Zn, Fe, Vib. Spectr., 2014, 71, 98-104. [ 41 ] Šimėnas, M.; Balciunas, S.; Ciupa, A.; Vilciauskas, L.; Jablonskas, D.; Kinka, M.; Sieradzki, A.; Samulionis, V.; Maczka, M.; Banys, J. Elucidation of dipolar dynamics and

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 34

nature of structural phases in [(CH3) 2NH2][Zn (HCOO) 3] hybrid perovskite framework, J. Mat. Chem. C., 2019, 7, 6779-6785. [42]Yadav R.; Diptikanta Swain D.; H. L. Bhat H. L.; Elizabeth S. Order-Disorder Phase Transition And MultiferroicBehaviour In A Metal Organic Framework Compound (CH3)2NH2Co(HCOO)3, J. App. Phys., 2016, 119, 064103. [43] Svane, K. L.; Forse, A. C.; Grey, C. P.; Kieslich, G.; Cheetham, A. K.; Walsh A.; Butler, K.T. How Strong Is the Hydrogen Bond in Hybrid Perovskites?, J. Phys. Chem. Lett.,2017,8, 6154–6159. [ 44 ] Sánchez-Andújar, M.; Presedo, S.; Yánez-Vilar, S.; Castro-García, S.; Shamir J.; Senarís-Rodríguez, M. A. Characterization Of The Order-Disorder Dielectric Transition In The Hybrid Organic-Inorganic Perovskite-Like Formate Mn(HCOO)(3)[(CH(3))(2)NH(2)], Inorg. Chem., 2010, 49, 1510–1516. [45] Jain P.; Stroppa A.; Nabok D.; Marino A.; Rubano A.; Paparo D.; Matsubara M.; Nakotte H.; Fiebig M.; Picozzi S.; Choi E. S.; Cheetham A. K.; Draxl C.; Dalal N. S.; Zapf V. S. Switchable Electric Polarization And Ferroelectric Domains In A Metal Organic-Framework, Quantum Mater., 2016, 1, 16012. [46] Boström, H. L. B.; Senn, M.S.; Goodwin, A. L. Recipes For Improper Ferroelectricity In Molecular Perovskites, Nat. Commun.,2018, 9, 2380. [47] Sieradzki, A.; Mączka, M.; Simenas, M.; Zaręba, J. K.; Gągor, A.; Balciunas, S.; Kinka, M.; Ciupa, A.; Nyk, M.; Samulionis, V.; Banys, J.; Paluch, M.; Pawlus, S. On the origin of ferroelectric structural phases in perovskite-like metal–organic formate,J. Mater. Chem. C, 2018, 6, 9420-9429.

30 ACS Paragon Plus Environment

Page 31 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

[48] Wang, X.-Y.; Gan, L.; Zhang, S.-W.; Gao, S. Perovskite-Like Metal Formates With Weak Ferromagnetism And As Precursors To Amorphous Materials, Inorg. Chem.,2004, 43, 4615–4625. [ 49 ] Clune, A. J.; Hughey, K. D.; Lee, C.; Abhyankar, N.; Ding, X.; Dalal, N. S.; Whangbo, M.-H.; Singleton, J.;

Musfelst, J. L. Magnetic Field-Temperature Phase

Diagram Of Multiferroic[(CH3)2NH2]Mn(HCOO)3,Phys. Rev. B,2017, 96, 104424. [50] Hughey, K.D.; Clune, A. J.; Yokosuk, M. O.; Al-Wahish, A.; O’Neal, K. R.; Fan, S.; Abhyankar, N.; Xiang, H.; Li, Z.; Singleton, J.; Dalal, N. S.; Musfeldt, J. L. Phonon mode links ferroicities in multiferroic[(CH 3)2NH2]Mn(HCOO)3, Phys. Rev. B,2017, 96, 180305. [ 51 ] Asaji, T.; Ashitomi, K.Phase Transition and Cationic Motion in a Metal–Organic Perovskite, Dimethylammonium Zinc Formate [(CH3)2NH2][Zn(HCOO)3],J. Phys. Chem. C, 2013, 117, 10185−10190. [52] Abhyankar, N.; Kweon, J. J.; Orio, M.; Bertaina, S.; Lee, M.; Choi, E. S.; Fu, R.; Dalal, N. S.Understanding Ferroelectricity in the Pb-Free Perovskite-Like Metal–Organic Framework [(CH3)2NH2]Zn(HCOO)3 : Dielectric, 2D NMR, and Theoretical Studies, J. Phys. Chem. C, 2017, 121, 6314–6322. [53] Kreisel, J.; Noheda B.; Dkhil, B. Phase transitions and ferroelectrics: revival and the future in the field, Phase Trans.,2009, 82, 633–661. [ 54 ] Mączka, M.;

Gągor, A.; Hermanowicz, K.; Sieradzki, A.; Macalik, L.; Pikul, A.

Structural, magnetic and phonon properties of Cr (III)-doped perovskite metal formate framework [(CH3)2NH2][Mn (HCOO)3],J. Sol. State Chem., 2016, 237, 150-158.

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 34

[55] Šimėnas, M.; Ciupa, A.; Usevicius, G.; Aidas, K.; Klose, D.; Jeschke, G.; Maczka, M.; Volkel, G.; Poppl, A.; Banys, J.Electron paramagnetic resonance of a copper doped [(CH3)2NH2][Zn(HCOO)3] hybrid perovskite Framework, Phys. Chem. Chem. Phys.,2018, 20, 12097-12105. [56] Sheldrick,G. M. A short history of SHELX, ActaCryst.,2008, A64, 112-122. [ 57 ] Mączka, M.; Hanuza, J.; Kamiński, A. A. Polarized IR, spontaneous and stimulated Raman spectra of Y(HCOO)3·2H2O single crystal — a new Raman laser material, J. Raman Spectrosc.,2006, 37, 1257-1264. [

58

] Szymborska-Małek, K.; Trzebiatowska-Gusowska, M.; Mączka, M.; Gągor, A.

Temperature-dependent

IR

and

Raman

studies

of

metal-organic

frameworks

[(CH3)2NH2][M(HCOO)3], M=Mg and Cd, Spectrochim. ActaA,2016, 159, 35-41. [59] Sletten, E.; Jensen, L. H. The crystal structure of dimethylammonium copper(II) formate, NH2(CH2)2[Cu(OOCH)3],ActaCryst.,1973, B29, 1752-1756. [60] Gonzalez-Nelson, A.; Coudert, F.-X.; Van Der Veen, M. A. Rotational Dynamics Of Linkers In Metal–Organic Frameworks, Nanomaterials,2019, 9, 330. [61] Shannon, R.D. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides, ActaCryst., 1976, A32, 751-767. [ 62] Sheldrick, G. M. Crystal structure refinement with SHELXL, ActaCryst. C, 2015, 71, 713-718. [63] Pyykkö, P.; Atsumi, M. Molecular Double-Bond Covalent Radii for Elements Li–E112. Chem. - Eur. J., 2009, 15, 12770–12779. [64]Janes, R.; Moore, E. A. Metal-ligand bonding, Royal Society of Chemistry, 2004.

32 ACS Paragon Plus Environment

Page 33 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

[ 65 ]Euler, H.; Barbier, B.; Kirfel, A.; Haselhoff, S.; Eggert, G.Crystal structure of trihydroxydicopperformate, Cu2(OH)3(HCOO), Z. Kristallogr., 2009, 224, 609-610. [66] Wang, Z.; Jain, P.; Choi, K.-Y.; van Tol, J.; Cheetham, A. K.; Kroto, H.W.; Koo, H.-J.; Zhou, H.; Hwang, J.; Choi, E. S.; Whangbo, M.-H.; Dalal, N. S. Dimethylammonium copper formate [(CH3)2NH2]Cu(HCOO)3: A metal-organic framework with quasi-onedimensional antiferromagnetism and magnetostriction, Phys. Rev. B,2013, 87, 224406. [67] Jonscher, A. K. Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983. [68] Jonscher, A. K. Universal Relaxation Law, Chelsea Dielectrics Press, London, 1996. [69 ] Jurlewicz, A.; Weron, K. A general probabilistic approach to the universal relaxation response of complex systems, Cell. Mol. Biol. Lett.,1999, 4 , 56-86. [70] Jurlewicz, A.; Weron, K. Relaxation of dynamically correlated clusters, J. Non-Cryst. Solids, 2002, 305, 112-121. [71] Jonscher, A. K.; Jurlewicz, A.; Weron, K. Stochastic schemes of dielectric relaxation in correlated-cluster systems, Contemp. Phys., 2003, 44, 329-333. [ 72 ] Asaji,T.; Ito, Y.; Fujimori, H.; Zhou, B. Ring-Puckering Motion Of Azetidinium Cations In A Metal–Organic Perovskite [(CH 2)3NH2][M(HCOO)3] (M = Zn, Mg)—A Thermal And 1H NMR Relaxation Study, J. Phys. Chem. C, 2019, 123(7), 4291-4298.

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