Raman Spectroscopy Studies on the Barocaloric Hybrid Perovskite [(CH3)4N][Cd(N3)3]

Temperature-dependent Raman scattering and differential scanning calorimetry were applied to the study of the hybrid organic-inorganic azide-perovskite [(CH3)4N][Cd(N3)3], a compound with multiple structural phase transitions as a function of temperature. A significant entropy variation was observed associated to such phase transitions, |∆S| ~ 62.09 J·kg−1 K−1, together with both a positive high barocaloric (BC) coefficient |δTt/δP| ~ 12.39 K kbar−1 and an inverse barocaloric (BC) coefficient |δTt/δP| ~ −6.52 kbar−1, features that render this compound interesting for barocaloric applications. As for the obtained Raman spectra, they revealed that molecular vibrations associated to the NC4, N3– and CH3 molecular groups exhibit clear anomalies during the phase transitions, which include splits and discontinuity in the phonon wavenumber and lifetime. Furthermore, variation of the TMA+ and N3– modes with temperature revealed that while some modes follow the conventional red shift upon heating, others exhibit an unconventional blue shift, a result which was related to the weakening of the intermolecular interactions between the TMA (tetramethylammonium) cations and the azide ligands and the concomitant strengthening of the intramolecular bondings. Therefore, these studies show that Raman spectroscopy is a powerful tool to gain information about phase transitions, structures and intermolecular interactions between the A-cation and the framework, even in complex hybrid organic-inorganic perovskites with highly disordered phases.


Introduction
Compounds that combine simultaneously organic and inorganic chemical groups are of great interest since they enlarge the range of structural possibilities that allow the coexistence and modulation of fundamental physical properties, increasing their multifunctional potential [1]. These hybrid clockwise), while along the b-axis, adjacent octahedra are oppositely rotated (alternating clockwise and counter-clockwise rotations); see Figure S2 of the supplementary materials. This unconventional tilting cannot exist in pure inorganic ABO3 perovskites.
Another interesting feature of this polymorph is the off-center shift of the TMA from the center of the cavities. At temperatures above 322 K, TMACdN3 transforms into a cubic phase (δ-phase), belonging to the Pm-3m space group (No. 221, Z = 1) [15], characterized by a large structural disorder of the azide ligands, where the rod-like N3 oscillates among four sites. Another significant feature is the disorder in TMA + , where the four (4) positions of the carbon ions in TMA + cation unfold into 12 positions, as illustrated in Figure 1.
In this paper, we try to gain more insight into such phase transformations and in the role of interactions between the A-cation and the framework in such structural transitions, an aspect that has not been analyzed so far in this compound. For this purpose, we use Raman spectroscopy as a tool that can be very powerful to study the mechanisms of structural phase transitions, to detect effects of order-disorder and to clarify how symmetry breaks; specifically, which vibrations, ions and molecular arrangements are strongly related to the given phase transitions [20][21][22][23][24][25][26][27]. Furthermore, from differential scanning calorimetric (DSC) measurements and structural data available in the literature, we estimate the barocaloric coefficients (|δTt/δP|) and entropy changes for each of these transitions to evaluate the potential of this compound as barocaloric material.

Basic Characterization and Deeper Insight into the Crystal Structure of TMACdN3
Room-temperature experimental X-ray powder diffraction results confirmed that the obtained sample of TMACdN3 is single phase as no impurities were present, and that at this temperature, it exhibits the expected crystal structure for the γ-phase. Details of the comparison between the experimental X-ray powder diffraction pattern of TMACdN3 at room temperature and the simulated X-ray diffraction pattern from single crystal measurements available in the literature [15] are given in the Supporting Information (see Figure S1).
On the other hand, to gain more insight into the phase transitions, we analyzed, in detail, the intermolecular interactions between the TMA cation and the [Cd(N3)3] − framework of the different polymorphs on the basis of the Hirshfeld surface analysis; see Fig. S3 of SI. This analysis shows that there are interactions between the H atoms of the TMA cation and the N atoms of the azide ligands (red regions at the Hirshfeld surface) both in the α-and γ-polymorphs. In addition, we observed that there are differences between the number of azide ligands involved in these interactions in each of these polymorphs. In the case of α-phase, the azide ligands (except the four along the a-axis) are all involved in the link with the TMA cation. Meanwhile, only two azide ligands (those located along Another interesting feature of this polymorph is the off-center shift of the TMA from the center of the cavities. At temperatures above 322 K, TMACdN 3 transforms into a cubic phase (δ-phase), belonging to the Pm-3m space group (No. 221, Z = 1) [15], characterized by a large structural disorder of the azide ligands, where the rod-like N 3 oscillates among four sites. Another significant feature is the disorder in TMA + , where the four (4) positions of the carbon ions in TMA + cation unfold into 12 positions, as illustrated in Figure 1.
In this paper, we try to gain more insight into such phase transformations and in the role of interactions between the A-cation and the framework in such structural transitions, an aspect that has not been analyzed so far in this compound. For this purpose, we use Raman spectroscopy as a tool that can be very powerful to study the mechanisms of structural phase transitions, to detect effects of order-disorder and to clarify how symmetry breaks; specifically, which vibrations, ions and molecular arrangements are strongly related to the given phase transitions [20][21][22][23][24][25][26][27]. Furthermore, from differential scanning calorimetric (DSC) measurements and structural data available in the literature, we estimate the barocaloric coefficients (|δT t /δP|) and entropy changes for each of these transitions to evaluate the potential of this compound as barocaloric material.

Basic Characterization and Deeper Insight into the Crystal Structure of TMACdN 3
Room-temperature experimental X-ray powder diffraction results confirmed that the obtained sample of TMACdN 3 is single phase as no impurities were present, and that at this temperature, it exhibits the expected crystal structure for the γ-phase. Details of the comparison between the experimental X-ray powder diffraction pattern of TMACdN 3 at room temperature and the simulated X-ray diffraction pattern from single crystal measurements available in the literature [15] are given in the Supporting Information (see Figure S1).
On the other hand, to gain more insight into the phase transitions, we analyzed, in detail, the intermolecular interactions between the TMA cation and the [Cd(N 3 ) 3 ] − framework of the different polymorphs on the basis of the Hirshfeld surface analysis; see Fig. S3 of SI. This analysis shows that there are interactions between the H atoms of the TMA cation and the N atoms of the azide ligands (red regions at the Hirshfeld surface) both in the αand γ-polymorphs. In addition, we observed that there are differences between the number of azide ligands involved in these interactions in each of these polymorphs. In the case of α-phase, the azide ligands (except the four along the a-axis) are all involved in the link with the TMA cation. Meanwhile, only two azide ligands (those located along the b-axis) are involved in such interactions in the case of the γ-phase. It is worth noting that these two different situations are also related to the location of the TMA inside of the pseudocuboctahedral cavity. In this context, as in the α-phase, the TMA cation is located at the center of the cavity and most of the azide ligands can interact with that cation. In contrast, in the case of the γ-phase, where the TMA cation is shifted from center of the cavity towards two of the azide ligands, those N 3 − are the only ones that can interact with it. During the discussion of the Raman results, we will show how these interactions between the TMA cation and the azide ligands, which are strongly influenced by temperature change, especially in the phase transition regions, are reflected and can be followed through the Raman spectra profile.

Thermal Characterization (DSC) and Barocaloric Parameters
DSC measurements confirm that the compound undergoes three reversible structural phase transitions as a function of temperature with T heating /T cooling = 270/263, 277/270 and 322/319 K, with an overlap of the peaks of the first two transitions (α→β and β→γ) and a sharp peak regarding the ferroelastic transition (γ→δ) (see Figure 2a). From the area under the peaks, we have obtained the isobaric enthalpy change ∆H ib for the α→β→γ transitions, which were analyzed jointly, and ferroelastic transition; see obtained values in Table 1. Additionally, we have also calculated the isobaric entropy change ∆S ib as a function of temperature using the following relation ∆S ib = is the heat flow measured at constant pressure, T is the temperature rate and T is the temperature, as it is shown in Figure 2b. The isobaric entropy change as a function of temperature grows abruptly until it reaches a local maximum plateau of~29.83 J·Kg −1 K −1 at the transition α→β→γ and~32.26 J·Kg −1 K −1 at the ferroelastic transition. Therefore, the total entropy change for the three phase transitions turns to be 62.09 J·kg −1 K −1 , which is in excellent agreement with the value reported in the literature [15,26].
Molecules 2020, 25, x 4 of 16 the b-axis) are involved in such interactions in the case of the γ-phase. It is worth noting that these two different situations are also related to the location of the TMA inside of the pseudocuboctahedral cavity. In this context, as in the α-phase, the TMA cation is located at the center of the cavity and most of the azide ligands can interact with that cation. In contrast, in the case of the γ-phase, where the TMA cation is shifted from center of the cavity towards two of the azide ligands, those N3 − are the only ones that can interact with it. During the discussion of the Raman results, we will show how these interactions between the TMA cation and the azide ligands, which are strongly influenced by temperature change, especially in the phase transition regions, are reflected and can be followed through the Raman spectra profile.

Thermal Characterization (DSC) and Barocaloric Parameters
DSC measurements confirm that the compound undergoes three reversible structural phase transitions as a function of temperature with Theating/Tcooling = 270/263, 277/270 and 322/319 K, with an overlap of the peaks of the first two transitions (αβ and βγ) and a sharp peak regarding the ferroelastic transition (γδ) (see Figure 2a). From the area under the peaks, we have obtained the isobaric enthalpy change ∆Hib for the αβγ transitions, which were analyzed jointly, and ferroelastic transition; see obtained values in Table 1. Additionally, we have also calculated the isobaric entropy change ∆Sib as a function of temperature using the following relation ∆ = is the temperature, as it is shown in Figure 2b. The isobaric entropy change as a function of temperature grows abruptly until it reaches a local maximum plateau of ~29.83 J·Kg −1 K −1 at the transition αβγ and ~32.26 J·Kg −1 K −1 at the ferroelastic transition. Therefore, the total entropy change for the three phase transitions turns to be 62.09 J·kg −1 K −1 , which is in excellent agreement with the value reported in the literature [15,26].   Table 1. Summary of thermodynamic parameters for the phase transitions of TMACdN 3 compound obtained from DSC analysis under heating and cooling. |∆H ib | is the isobaric enthalpy change, |∆S ib | is the isobaric entropy change, N is the number of sites in the disordered phase and δT t /δP is the barocaloric coefficient.

Parameters
Heating Cooling As in order-disorder phase transitions, ∆S is given by R ln(N) with N = (n 2 /n 1 ), where n 2 and n 1 are the number of configurations in each polymorph and R is the gas constant (8.314 J mol −1 K −1 ), we have estimated, from the heating data, an N = 2.9 and 2.5 for the α→β→γ transition and ferroelastic, respectively. All the values of enthalpy change ∆H, entropy change ∆S and N under heating and cooling are summarized in Table 1.
Additionally, following the procedure reported in the literature [7], we have estimated different barocaloric parameters to evaluate the potential of this hybrid perovskite as a barocaloric material.
In this context we have to note that TMACdN 3 shows relevant features, which, in principle, render it a good candidate to show high barocaloric effects, especially as it has a relative large reversible ferroelastic structural transition, whose critical temperature is close to room temperature, making it highly desirable for practical applications; the intrinsic flexibility of the azide ligand, which is part of the framework, makes it susceptible to large volume variations under applied external pressure.
To estimate the barocaloric (BC) coefficient of TMACdN 3 , we have used the Clausius-Clapeyron method, which is a widely used indirect method in the case of caloric materials [7]. Taking into account the following expression, (δTt/δP) = (∆v/∆S), where ∆v is the volume change at the phase transition and ∆S is the entropy change of the phase transition, we calculate the BC coefficient from our calorimetric results (on heating) as well the structural data (volume) in the vicinity of the structural transition available in the literature [28]. Following this method, we have estimated the barocaloric coefficient for the α→β→γ phase transition and for γ→δ, as shown in Table 1. As it can be seen there, the two barocaloric coefficients are very different, not only in magnitude (one almost double than the other) but also in sign. In this context, while the α→β→γ phase transition exhibits a positive, conventional BC coefficient (which means that the γ phase heats up when adiabatically squeezed and cools down when pressure is released close to this phase transition temperature), the ferroelastic γ→δ transition displays a negative, that is, inverse, BC coefficient (that is, the γ phase cools down when pressure is applied and heats up when it is released close to the ferroelastic phase transition temperature).
For the α→β→γ phase transitions, the BC coefficient is 12.39 K kbar −1 , which is similar to that exhibited by the related azide hybrid perovskite TMAMnN 3 [18]. In any case, it is worth to note that the BC coefficient of TMACdN 3 is very large in comparison with BC inorganic compounds (such as alloys and oxides), which typically exhibit values inferior to 1 K kbar −1 [29]. Very interestingly, the ferroelastic transition displays an inverse BC coefficient, which is very scarce, and few materials are known with this property. Therefore, the BC parameters indicate that TMACdN 3 is an interesting material from BC applications with an adequate working temperature, close to room temperature between 260 and 320 K, and isobaric entropy change values almost similar to those reported for related [TPrA][Mn(dca) 3 ] hybrid perovskite, whose values is 38.1 J·Kg −1 K −1 (until now the highest report value for a BC hybrid perovskite). Figure 3 shows the Raman spectrum obtained for TMACdN 3 at room temperature, which, in fact, is rather similar to that observed for TMAMnN 3 and DMAMnN 3 [24] compounds. According to group theory, considering the irreducible representations of the group factor C 2h (2/m) and the occupations of the Wyckoff sites of the space group C 2h 2 (P2 1 /m), 72 Raman active modes are predicted

Room Temperature Raman Spectrum
. Among those, 33 modes were observed, being a reasonable number considering that in these compounds, a large grouping of modes is expected in narrow bands of the spectrum. The vibrational modes investigated are mainly attributed to internal vibrations of the TMA + cations, azide anions and lattice vibrations [24]. Most internal modes of TMA + cations and azide ligands are observed in distinct regions of the spectrum, which facilitates the assignment and comparison with similar compound spectra. Thus, our assignment of the observed modes was based on Raman investigations of similar compounds available in literature [23,[29][30][31] and it is summarized in Table 2.
Molecules 2020, 25, x 6 of 16 Figure 3 shows the Raman spectrum obtained for TMACdN3 at room temperature, which, in fact, is rather similar to that observed for TMAMnN3 and DMAMnN3 [24] compounds. According to group theory, considering the irreducible representations of the group factor (2/m) and the occupations of the Wyckoff sites of the space group (P21/m), 72 Raman active modes are predicted (Γ = 38 ⨁ 34 ). Among those, 33 modes were observed, being a reasonable number considering that in these compounds, a large grouping of modes is expected in narrow bands of the spectrum. The vibrational modes investigated are mainly attributed to internal vibrations of the TMA + cations, azide anions and lattice vibrations [24]. Most internal modes of TMA + cations and azide ligands are observed in distinct regions of the spectrum, which facilitates the assignment and comparison with similar compound spectra. Thus, our assignment of the observed modes was based on Raman investigations of similar compounds available in literature [23,[29][30][31] and it is summarized in Table 2. As can be seen there, at frequencies below 300 cm −1 , lattice modes are mainly observed and include translational and librational modes of the TMA + cations, N3 − organic groups as well as those of Cd 2+ ions. In this region, less pure modes are also observed, with quite representative intensities, such those at 220 and 274 cm −1 , which can be classified as N3 − librations and a combination of CH3 group twisting with an Cd ion translation, respectively.

Room Temperature Raman Spectrum
The intermediate-and high-frequency regions are dominated by internal modes. A rather prominent mode attributed to the symmetric stretching of the NC4 group is observed at approximately 758 cm −1 . The region between 1000-1500 cm −1 exhibits several low-intensity modes mainly due to CH3 rocking (ρ modes) observed at about 1047, 1171, 1218 and 1359 cm −1 and δ-bending (scissoring) of CH3 group (δasCH3 δsCH3) as the mode at 1453 cm −1 . This band also includes the azide group symmetric stretching ( mode) at 1359 cm −1 , which is a very intense and important mode for monitoring the azide ligands N3 − (see Table 2).
In the higher-frequency region, above 2000 cm −1 , internal modes related to TMA + prevail, such as the symmetric stretching of the CH3 group and combinations of symmetric stretching and As can be seen there, at frequencies below 300 cm −1 , lattice modes are mainly observed and include translational and librational modes of the TMA + cations, N 3 − organic groups as well as those of Cd 2+ ions. In this region, less pure modes are also observed, with quite representative intensities, such those at 220 and 274 cm −1 , which can be classified as N 3 − librations and a combination of CH 3 group twisting with an Cd ion translation, respectively. The intermediate-and high-frequency regions are dominated by internal modes. A rather prominent mode attributed to the symmetric stretching of the NC 4 group is observed at approximately 758 cm −1 . The region between 1000-1500 cm −1 exhibits several low-intensity modes mainly due to CH 3 rocking (ρ modes) observed at about 1047, 1171, 1218 and 1359 cm −1 and δ-bending (scissoring) of CH 3 group (δ as CH 3 δ s CH 3 ) as the mode at 1453 cm −1 . This band also includes the azide group symmetric stretching (ν 1 mode) at 1359 cm −1 , which is a very intense and important mode for monitoring the azide ligands N 3 − (see Table 2). In the higher-frequency region, above 2000 cm −1 , internal modes related to TMA + prevail, such as the symmetric stretching of the CH 3 group and combinations of symmetric stretching and asymmetric stretching of this methyl group. As we will show, these medium-intensity modes are very sensitive to disorder and modifications in the chemical environment of TMA during phase transitions. In this region, we highlight the 2953 and 2978 cm −1 modes that are attributed to pure CH 3 symmetric stretching vibrations and those observed at 2921 and 3032 cm −1 that correspond to mixed symmetric and asymmetric stretching modes of the CH 3 group.

Raman Spectra as a Function of Temperature
The factor group analysis of the fundamental modes and correlation diagram for the low temperature α-phase (space group C2/c) are presented in Table S1  compound [24]. Furthermore, since the δ-phase of TMCdN 3 is highly disordered, its analysis is not given here. Figures 4 and 5 show representative normalized Raman spectra of TMACdN 3 from 295 K to 365 K in the frequency range 30 to 3100 cm −1 and from 80 K to 290 K in the range 50 to 3300 cm −1 , respectively. In both cases, the dashed lines indicate the critical temperatures for the phase transitions according to DSC, T γ→δ(heating) = 322 K ( Figure 5) and T γ→β→α(cooling) = 265 K, temperatures at which significant changes in the Raman spectra also occur (see below).
given here. Figures 4 and 5 show representative normalized Raman spectra of TMACdN3 from 295 K to 365 K in the frequency range 30 to 3100 cm −1 and from 80 K to 290 K in the range 50 to 3300 cm −1 , respectively. In both cases, the dashed lines indicate the critical temperatures for the phase transitions according to DSC, Tγδ(heating) = 322 K ( Figure 5) and Tγβα(cooling) = 265 K, temperatures at which significant changes in the Raman spectra also occur (see below).
As shown in Figures 4 and 5, the main changes observed in these spectra as temperature increases can be summarized as follows: in first place, a broadening of the modes and, in general, a decrease in their intensity-see, for example, Figure 5a. Especially interesting is the region of 1312−1402 cm −1 , corresponding to the azide group νs modes (ν1), where the band, which is split at low temperatures, seems to merge into one at T (  ), while a new shoulder at 1366 cm −1 starts to develop in the vicinity of this critical temperature; see Figure 5c. For higher temperatures (Figure 4c), a new approximation of the azide group νs modes (ν1) at 1359 and 1366 cm −1 takes place, finally giving rise to a broad band.  Figure 5b,d, more subtle changes may be noticed and will be discussed below in more detail.
In order to perform a more detailed analysis of the behavior of the phonons during the temperature-induced multiple structural phase transitions in TMACdN3, we show, in Figures 6 and  7, the behavior of the most intense modes which were more susceptible to structural changes. In addition, we also include the temperature dependence of their full width at half-maximum (FWHM), which depends on the phonon's lifetime in the lattice and their anharmonicities. As it is well-known, FWHM is very sensitive to structural disorder, whose presence contributes to reducing the phonon's lifetime and consequently increases the width of the spectral bands [32][33][34][35].  Figure 5b,d, more subtle changes may be noticed and will be discussed below in more detail.
As shown in Figures 4 and 5, the main changes observed in these spectra as temperature increases can be summarized as follows: in first place, a broadening of the modes and, in general, a decrease in their intensity-see, for example, Figure 5a. Especially interesting is the region of 1312−1402 cm −1 , corresponding to the azide group ν s modes (ν 1 ), where the band, which is split at low temperatures, seems to merge into one at T(γ α), while a new shoulder at 1366 cm −1 starts to develop in the vicinity of this critical temperature; see Figure 5c. For higher temperatures (Figure 4c), a new approximation of the azide group ν s modes (ν 1 ) at 1359 and 1366 cm −1 takes place, finally giving rise to a broad band.
In order to perform a more detailed analysis of the behavior of the phonons during the temperature-induced multiple structural phase transitions in TMACdN 3 , we show, in Figures 6  and 7, the behavior of the most intense modes which were more susceptible to structural changes. In addition, we also include the temperature dependence of their full width at half-maximum (FWHM), which depends on the phonon's lifetime in the lattice and their anharmonicities. As it is well-known, FWHM is very sensitive to structural disorder, whose presence contributes to reducing the phonon's lifetime and consequently increases the width of the spectral bands [32][33][34][35].  Figure 6 shows the behavior of the wavenumber and FWHM of the modes related to the azide group which can be attributed mainly to the symmetrical stretching vibrations νs(ν1)N3 − . In particular, the very intense band at 1359 cm −1 is presented as the main mode because it remains present, with slight modifications, in all structural phases. As qualitatively explained before, for T < 265 K in the low-temperature phase, a splitting is observed and a new mode emerges at 1355 cm −1 , while the main mode experiences a red shift to 1361 cm −1 . For 265 < T(K) < 323, the main mode experiences a blue shift back to 1359 cm −1 and a new band appears at 1366 cm −1 , showing the αγ phase transition. In addition, discontinuities in the phonon energy at 1359 and 1366 cm −1 are observed at approximately 323 K (under heating), where the second structural phase transition γδ occurs. A strong narrowing and discontinuity in the width of the modes 1359 and 1366 cm −1 are also observed at 323 K; see Figure  6.
We rationalize the observed behavior as follows: at low temperatures, below 265 K, the splitting of the observed symmetrical stretching vibrations νs(ν1)N3 − reflects the presence of two groups of azide ligands, which mainly differ in the degree of interaction with the H atoms of the TMA cation. Those with stronger azide-H-TMA interactions (and thus with more weakened and more enlarged intraligand N-N bonds) give rise to a lower wavenumber, while those that do not interact with the TMA cation through the H atoms (and thus with stronger N-N intraazide bonds) give rise to higher wavenumber bands; see Figure S4 of supplementary materials. The assignment of azide ligands is reinforced by the temperature dependence of both ligands. The one with stronger interactions shows an increase of wavenumber on heating, which is an anomalous behavior, due to the weakening of this interaction upon heating.
At 265 K, the structural transformation and the concomitant changes in the distances and angles in the azide-framework interaction result in the breaking of H bonds between the azides that were initially interacting with the framework. Furthermore, a majority of azides get liberated from such bonding and strengthen their intraligand N-N bonds, giving rise to the appearance of a higher number shoulder (about 1367 cm −1 ); see Figure S4 of supplementary materials. We suggest that the off-center shift of the TMA seems to play an important role at the observed large splitting of the azide group symmetrical stretching vibrations. Again, the temperature dependence of both modes upon   Figure 6. We rationalize the observed behavior as follows: at low temperatures, below 265 K, the splitting of the observed symmetrical stretching vibrations ν s (ν 1 )N 3 − reflects the presence of two groups of azide ligands, which mainly differ in the degree of interaction with the H atoms of the TMA cation. Those with stronger azide-H-TMA interactions (and thus with more weakened and more enlarged intraligand N-N bonds) give rise to a lower wavenumber, while those that do not interact with the TMA cation through the H atoms (and thus with stronger N-N intraazide bonds) give rise to higher wavenumber bands; see Figure S4 of supplementary materials. The assignment of azide ligands is reinforced by the temperature dependence of both ligands. The one with stronger interactions shows an increase of wavenumber on heating, which is an anomalous behavior, due to the weakening of this interaction upon heating. At 265 K, the structural transformation and the concomitant changes in the distances and angles in the azide-framework interaction result in the breaking of H bonds between the azides that were initially interacting with the framework. Furthermore, a majority of azides get liberated from such bonding and strengthen their intraligand N-N bonds, giving rise to the appearance of a higher number shoulder (about 1367 cm −1 ); see Figure S4 of supplementary materials. We suggest that the off-center shift of the TMA seems to play an important role at the observed large splitting of the azide group symmetrical stretching vibrations. Again, the temperature dependence of both modes upon heating is in agreement with the proposed assignment. The non-interacting azide ligands exhibit a red shift on heating due to the weakening of N-N bond interactions. In contrast, the interacting azide ligand shows a blue shift on heating due to the weakening of the intermolecular interaction and the stronger intramolecular bonding.
Above T > 332 K, the dynamic forming and breaking of much weaker azide-H-TMA bonds could be the reason for the broad bands observed above that critical temperature.
Furthermore, the strong change observed in the width of the modes could be reflecting variations in the degree of structural disorder in the azide ligands, similar to that observed for TMAMnN 3 and NaN 3 [24,36] crystals. Furthermore, the variation in the width of the mode observed at 1359 cm −1 during the γ→δ phase transition is abrupt, with a discontinuity, which is, in fact, consistent with the strong increase in the disorder in the azide ligands in the δ phase.
It should be noted that these results differ significantly from those obtained in the Mn azide [24], where a much broader Raman band for the symmetrical stretching vibration of the azide ligand did not allow to see these changes as a function of temperature. heating is in agreement with the proposed assignment. The non-interacting azide ligands exhibit a red shift on heating due to the weakening of N-N bond interactions. In contrast, the interacting azide ligand shows a blue shift on heating due to the weakening of the intermolecular interaction and the stronger intramolecular bonding. Above T > 332 K, the dynamic forming and breaking of much weaker azide-H-TMA bonds could be the reason for the broad bands observed above that critical temperature.
Furthermore, the strong change observed in the width of the modes could be reflecting variations in the degree of structural disorder in the azide ligands, similar to that observed for TMAMnN3 and NaN3 [24,36] crystals. Furthermore, the variation in the width of the mode observed at 1359 cm −1 during the γδ phase transition is abrupt, with a discontinuity, which is, in fact, consistent with the strong increase in the disorder in the azide ligands in the δ phase.
It should be noted that these results differ significantly from those obtained in the Mn azide [24], where a much broader Raman band for the symmetrical stretching vibration of the azide ligand did not allow to see these changes as a function of temperature. On the other hand, Figure 7 shows the behavior of the wavenumber and FWHM of the modes observed at 220, 274 and 758 cm −1 for the entire temperature range studied. Through the anomalies observed in the behavior of these modes, we can also clearly identify the two phase transitions (αγ and γδ) occurring at approximately 265 K (under cooling) and 323 K (under heating), both temperatures being in excellent agreement with the DSC measurements. As for the first phase transition (αγ), it is observed that the modes at 220 and 274 cm −1 follow a natural softening behavior with an increase in temperature, to subsequently suffer an abrupt increase in energy, an anomalous blue shift of ~4cm −1 , followed by a new softening trend after the transition. Such variations can be mainly attributed to structural changes perceived in the LN3 − and τCH3 T′(Cd) vibrations, respectively, probably related to the cooperative tilting of the [CdN6] octahedra and concomitant framework distortion that occur at that temperature. As for the behavior of the FWHM of these modes, a sudden broadening is observed with increasing temperature, in agreement with the slight order-disorder effect in the azide ligand in the intermediate phase. On the other hand, Figure 7 shows the behavior of the wavenumber and FWHM of the modes observed at 220, 274 and 758 cm −1 for the entire temperature range studied. Through the anomalies observed in the behavior of these modes, we can also clearly identify the two phase transitions (α→γ and γ→δ) occurring at approximately 265 K (under cooling) and 323 K (under heating), both temperatures being in excellent agreement with the DSC measurements. As for the first phase transition (α→γ), it is observed that the modes at 220 and 274 cm −1 follow a natural softening behavior with an increase in temperature, to subsequently suffer an abrupt increase in energy, an anomalous blue shift of 4cm −1 , followed by a new softening trend after the transition. Such variations can be mainly attributed to structural changes perceived in the LN 3 − and τCH 3 T (Cd) vibrations, respectively, probably related to the cooperative tilting of the [CdN 6 ] octahedra and concomitant framework distortion that occur at that temperature. As for the behavior of the FWHM of these modes, a sudden broadening is observed with increasing temperature, in agreement with the slight order-disorder effect in the azide ligand in the intermediate phase. Regarding the γδ transition, an abrupt variation in the width of the modes at 220 and 274 cm −1 , which undergo an increase in width of ~15 cm −1 , is observed in contrast to the variation of the same modes at the αγ transition. This clearly demonstrates a direct relationship between the FWHM change and the degree of structural disorder since the δ phase exhibits high structural disorder in the TMA cations and in all crystallographic directions for the N3 − ligand. On the other hand, the anomalies observed in the wavenumber were more subtle. Figure 7 also shows the temperature dependence of the wavenumber and FWHM of the mode at 758 cm −1 , characteristic for the NC4 group (TMA), which is split into two modes at temperatures below 265 K as a result of symmetry reduction and merges into a single one above that critical temperature. It is important to highlight that during the αγ transition, the width of this mode is characterized by a strong discontinuity, at difference with the behaviors observed for the widths of the modes at 220 and 274 cm −1 . This indicates that short-range disorder effects on TMA cations must be present in the αγ transition since the long-range subtle structural changes could not justify such a significant variation in FWHM. Furthermore, during the γδ phase transition, an anomalous hardening of this mode is observed with increasing temperature, behavior which can be explained by the shortening of the C-N bonds (from 1.486 to 1.492 Å in the α-phase to 1.465 to 1.486 Å in the γphase and 1.411 Å in δ phase [14]), probably related to a strengthening of the N-C bond upon weakening of the TMA-azide interaction.
Finally, Figure 8 shows the temperature dependence of the wavenumber and FWHM of the modes associated with the CH3 group observed at 2921, 2952 and 3032 cm −1 . As it can be seen, the frequency of the 2921 and 2952 cm −1 modes has a very similar behavior with temperature, characterized by the anomalous hardening of these modes as temperature increases. Meanwhile, those at higher frequencies (3032 cm −1 ) follow the expected behavior as a function of temperature, even if with a sharp jump at the phase transitions.
As for the 2921 and 2952 cm −1 modes, their anomalous behavior is probably related to the fact that they correspond to TMA cations that are interacting with the azides in the framework. In this case, the data reveal a strengthening of the intraatomic C-H bond as temperature increases and the azide-H-TMA interaction decreases. In addition, both modes exhibit anomalies that can be easily identified during the αγ and γδ phase transitions. The first anomaly, observed at approximately 323 K, is characterized by an attenuation in the tendency of softening of the modes with temperature Regarding the γ→δ transition, an abrupt variation in the width of the modes at 220 and 274 cm −1 , which undergo an increase in width of~15 cm −1 , is observed in contrast to the variation of the same modes at the α→γ transition. This clearly demonstrates a direct relationship between the FWHM change and the degree of structural disorder since the δ phase exhibits high structural disorder in the TMA cations and in all crystallographic directions for the N 3 − ligand. On the other hand, the anomalies observed in the wavenumber were more subtle. Figure 7 also shows the temperature dependence of the wavenumber and FWHM of the mode at 758 cm −1 , characteristic for the NC 4 group (TMA), which is split into two modes at temperatures below 265 K as a result of symmetry reduction and merges into a single one above that critical temperature. It is important to highlight that during the α→γ transition, the width of this mode is characterized by a strong discontinuity, at difference with the behaviors observed for the widths of the modes at 220 and 274 cm −1 . This indicates that short-range disorder effects on TMA cations must be present in the α→γ transition since the long-range subtle structural changes could not justify such a significant variation in FWHM. Furthermore, during the γ→δ phase transition, an anomalous hardening of this mode is observed with increasing temperature, behavior which can be explained by the shortening of the C-N bonds (from 1.486 to 1.492 Å in the α-phase to 1.465 to 1.486 Å in the γ-phase and 1.411 Å in δ phase [14]), probably related to a strengthening of the N-C bond upon weakening of the TMA-azide interaction.
Finally, Figure 8 shows the temperature dependence of the wavenumber and FWHM of the modes associated with the CH 3 group observed at 2921, 2952 and 3032 cm −1 . As it can be seen, the frequency of the 2921 and 2952 cm −1 modes has a very similar behavior with temperature, characterized by the anomalous hardening of these modes as temperature increases. Meanwhile, those at higher frequencies (3032 cm −1 ) follow the expected behavior as a function of temperature, even if with a sharp jump at the phase transitions. the structural transitions. Interestingly, the anomalies observed in FWHM in these last three modes related to TMA reinforce that short-range disorder effects are present during the αγ structural phase transition and are perceived in the vibrations of the CH3 and NC4 groups, as previously observed in Figure 7. Variations in the short-range configuration certainly contribute to the experimental N value (∆S = R ln (N)) during the αγ transition, showing higher values than those observed for the ferroelastic transition (see Table 1).

Synthesis
Block-shaped single crystals of TMACdN3 were obtained by the slow evaporation method as previously reported [15]. An aqueous solution (10 mL) of NaN3 (390 mg, 6 mmol) and (CH₃)₄NCl (630 mg, 3 mmol) was mixed with an aqueous solution (5 mL) of Cd(NO3) 4H2O (154 mg, 0.5 mmol). The resulting solution was filtered through a sieve (0.22 μm) and the obtained clear solution was kept at room temperature. After 3 days, transparent crystals were observed at the bottom of the glass. As for the 2921 and 2952 cm −1 modes, their anomalous behavior is probably related to the fact that they correspond to TMA cations that are interacting with the azides in the framework. In this case, the data reveal a strengthening of the intraatomic C-H bond as temperature increases and the azide-H-TMA interaction decreases. In addition, both modes exhibit anomalies that can be easily identified during the α→γ and γ→δ phase transitions. The first anomaly, observed at approximately 323 K, is characterized by an attenuation in the tendency of softening of the modes with temperature reduction. After the second transition at~265 K (under cooling), the softening of these modes becomes quite pronounced in good agreement with the changes commented in the azides related to the azide-H-TMA interaction. Such anomalies can also be observed in the width of these modes, which show prominent changes at~265 K and 323 K. In particular, the width of the mode 2952 cm −1 undergoes a strong discontinuity (~8 cm −1 ) at approximately 265 K, which can be associated with a structural disorder of the CH 3 group, marking the first transition. Above 323 K, a discontinuity in the width of this mode reveals that the second transition is strongly influenced by the disorder effects of the CH 3 group. Regarding the band observed at 3032 cm −1 , a splitting of modes occurs at temperatures below 265 K and a slight change in the trend in the wavenumber during the ferroelastic transition. The width of the mode at 3032 cm −1 also presents clear anomalies near to critical temperatures, proving the structural transitions. Interestingly, the anomalies observed in FWHM in these last three modes related to TMA reinforce that short-range disorder effects are present during the α→γ structural phase transition and are perceived in the vibrations of the CH 3 and NC 4 groups, as previously observed in Figure 7. Variations in the short-range configuration certainly contribute to the experimental N value (∆S = R ln (N)) during the α→γ transition, showing higher values than those observed for the ferroelastic transition (see Table 1).

Synthesis
Block-shaped single crystals of TMACdN 3 were obtained by the slow evaporation method as previously reported [15]. An aqueous solution (10 mL) of NaN 3 (390 mg, 6 mmol) and (CH 3 ) 4 NCl (630 mg, 3 mmol) was mixed with an aqueous solution (5 mL) of Cd(NO 3 ) 4H 2 O (154 mg, 0.5 mmol). The resulting solution was filtered through a sieve (0.22 µm) and the obtained clear solution was kept at room temperature. After 3 days, transparent crystals were observed at the bottom of the glass.

Powder X-ray Diffraction
Powder X-ray diffraction (PXRD) patterns of the obtained powders and of grounded single-crystals were collected in a Siemens D-5000 diffractometer (Aubrey, TX, USA) using Cu K α radiation at room temperature.

Hirshfeld Surface Analysis
Identification of close contacts between the framework and the TMA cations in the cavities was carried out by means of Hirshfeld surface analysis using CIF (Crystallographic Information Framework) data [15] and the CrystalExplorer 17.5 software [37].

Differential Scanning Calorimetry-DSC
Differential scanning calorimetric (DSC) analyses were carried out in a TA Instruments DSC Q-2000 (Waters, Cerdanyola del Valles, Spain) by heating and cooling the samples under a nitrogen atmosphere, during several cycles at 10 K/min.

Temperature-Dependent Raman Spectroscopy
The temperature-dependent Raman measurements were carried out in the 80-373 K range using a Horiba Jobin-Yvon T64000 triple-grating spectrometer (Horiba/Jobin Yvon/ISA, Edison, NJ, USA). For the high-and low-temperature measurements, a Linkam TS1200 heating stage and a CTI-Cryogenic M-22 closed-cycle He refrigerator system were used, respectively. A 532.0 nm radiation from a Diode-Pumped Solid-State Laser (DPSSL) (Horiba/Jobin Yvon/ISA, Edison, NJ, USA), operating at 14 mW, was used as the excitation source. The spectra were collected in back-scattering geometry with a resolution of 2 cm −1 on heating, in the case of the high T measurements, and upon cooling, in the case of the low T measurements. An Olympus BX41 microscope equipped with a 20× long working distance (WD = 20.4 mm) objective lens was used to focus the laser beam on the sample surface (Olympus, Center Valley, PA, USA), and the Raman signal was detected with an N2-cooled Charge-Coupled Device (CCD) (Olympus, Center Valley, PA, USA).

Conclusions
Crystals of the azide compound [N(CH 3 ) 4 ][Cd(N 3 ) 3 ] belonging to the hybrid organic-inorganic perovskite family were obtained by the slow evaporation method. DSC measurements demonstrated that the compound experiences multiple structural transitions, with a total entropy change of |∆S| 62.09 J·kg −1 K −1 . The estimated barocaloric coefficient, (δT t /δP), gives values of 12.39 and −6.52 K kbar −1 for the α→β→γ and the ferroelastic phase transitions, respectively. These values are very large in comparison with BC inorganic compounds (such as alloys and oxides) and similar to those found in the analogous TMAMnN 3 hybrid perovskite [18]. Very interestingly, the ferroelastic transition displays an inverse BC coefficient, which is very scarce, and few materials are known to exhibit this behavior. In addition, its working temperature is close to room temperature, between 260 and 320 K. All these findings indicate that TMACdN 3 is an interesting material for BC applications.
On the other hand, a detailed study of the temperature dependence of Raman modes between 80 and 373 K was carried out. In this context, the internal vibration groups of the TMA cation and the N 3 − azide ligand and the lattice vibrations were distinguished in specific spectral bands, allowing classifications of the modes and individualized monitoring of the vibrations by molecular groups as a function of temperature. In the vicinity of the critical temperatures of the α→γ and γ→δ transitions, the vibrational frequencies and FWHMs exhibited clear anomalies, indicating the onset of the first-order structural phase transitions. From analysis of the variation of TMA and azide modes with temperature, it was observed that many modes follow the conventional red shift upon heating, while other modes exhibit an unconventional blue shift, which were related to the weakening of intermolecular interactions and the strengthening of intramolecular bonding, respectively. Abrupt variations in the width of the modes related to TMA + , particularly in the vibrations of symmetric and asymmetric stretching of CH 3 molecular group and the symmetric stretching of the NC 4 group, indicate that short-range disorder effects are present during the α→γ structural transition.
These results show that Raman spectroscopy is a powerful tool to gain information about phase transitions and intermolecular interactions between the A-cation and the framework, even at disordered phases, in complex hybrid organic-inorganic perovskites.
Supplementary Materials: The following are available online, Figure S1: (above) Experimental X-ray powder diffraction pattern of the TMACdN3 sample at room temperature, and (below), the simulated X-ray powder diffraction pattern of TMACdN3 obtained from the single crystal measured data, Figure