Electromechanical properties of uniaxial polar ionic plastic crystal [(C2H5)4N][FeBrCl3]

Ferroelectric plastic crystals are an emerging class of materials that combine room temperature ferroelectricity and piezoelectricity with a high temperature plastic mesophase prior to melting. These materials offer possibilities for accessing different property parameter spaces from the state-of-the-art metal oxide and polymer ferroelectrics. Tetraethylammonium bromotrichloroferrite, [(C2H5)4N][FeBrCl3], has a unipolar wurtzite-like structure and thus may have potential for small but stable piezoelectric coefficients like the iso-symmetrical AlN. In this study, density functional theory was used to compute elastic compliance, piezoelectric coefficients, and dielectric constant values. Single crystals grown from aqueous solutions were evaluated via single crystal synchrotron x-ray diffraction, impedance spectroscopy and high and weak-field electromechanical characterization. Diffraction studies revealed that the anion tetrahedra orientated preferentially so that the Br− ion had a 30% alignment with the polarization vector. Electromechanical measurements found piezoelectric coefficients in the 5–9 pC N−1 and pm V−1 range. The piezoelectric coefficient (d 33) was most stable with 3.4% variation between 0.4 and 90 Hz and 0.5 and 3 V. Additional piezoelectric stability measurements were made as a function of DC bias field and temperature. Impedance measurements indicate contributions from either intrinsic effects unique to ionic plastic crystals, such as molecular rotation, or the extrinsic effect of electrode interfaces, both of which can play a role in the electromechanical response of the materials. The results show that [(C2H5)4N][FeBrCl3] has potential as a small signal piezoelectric that has a softer elastic moduli than AlN but a stiffer moduli than polyvinylidene fluoride, and thus occupies a unique parameter space.


Introduction
Ferroelectric materials with switchable spontaneous electric polarizations and electromechanical responses are essential materials for data storage, data transfer, energy harvesting and microelectromechanical devices [1][2][3][4].Ferroelectric plastic crystals (FPC) have recently emerged as an exciting new class of ferroelectrics which combine ferroelectricity with plastic crystal properties [5][6][7][8].The plastic crystal distinction means that the materials consist of weakly bonded, that is non-ionic/non-covalently bonded, molecular components that can gain orientational entropy at elevated temperatures and become plastically deformable [9].The combination of ferroelectricity with pliability in FPCs may open the door to novel device fabrication while the material properties fill an open parameter space.
The state of the art ferroelectric materials are dominated by brittle metal oxides like Pb(Zr,Ti)O 3 (PZT), metal nitrides like AlN-based materials, and soft polymers such as polyvinylidene fluoride (PVDF) [1,4,10].More recently ferroelectric organic-inorganic perovskites such as TMCM-CdCl 3 have emerged as a class of materials with impressive piezoelectric coefficients, as high as 220 pC N −1 , and these materials now hold a new gold standard for molecular ferroelectrics [11].By comparison with the metal oxides, nitrides and polymers, FPCs have lower processing temperatures, are easily precipitated from solutions, have greater compositional diversity with fewer rare elements, and are soluble; giving them the possibility of being dissolved and recycled at the end of their useful life, an advantageous property from a sustainability perspective.
Tetraethylammonium bromotrichloroferrite (TEAFBC), [(C 2 H 5 ) 4 N][FeBrCl 3 ], is a known plastic crystal material.The plastic crystal distinction was made due to the presence of a high enthalpy (65.7 Jg −1 ) and entropy (151.5 JK −1 Kg −1 ) solid-solid phase transition at 150 • C where the high temperature mesophase exhibits the requisite high symmetry and high molecular orientational disorder, as confirmed by differential scanning calorimetry, x-ray diffraction and total scatter pair distribution function measurements.This data is published elsewhere by Walker et al [12].While in this high temperature mesophase the material exhibits the signature plastic deformability synonymous with plastic crystals.
TEAFBC has a hexagonal crystal structure with P6 3 mc symmetry, and is isosymmetric with the commercially significant AlN-based materials [12][13][14][15].Because of the P6 3 mc symmetry, TEAFBC has only two crystallographically allowable polarization directions, parallel and antiparallel with the c axis, and thus has a uniaxial polarization.While TEAFBC has not been demonstrated to be ferroelectric, the recent discovery of polarization reversibility in uniaxial wurtzite's based on AlN means that the crystal structure of TEAFBC does not exclude it from having a switchable polarization.[16,17] Uniaxial ferroelectrics like AlN make excellent radio frequency filters, resonators and antenna due to their small but stable electromechanical response [3,14].This stability of the piezoelectric response as a function of frequency, electric field, stress, and temperature, arises due to the lack of contributions from ferroelastic (non-180 degree) domain walls [18][19][20].Ferroelastic (non-180 • ) domain walls contribute to as much as 50%-70% of the piezoelectric coefficient in key commercial ferroelectrics like donor (e.g.Nb) doped PZT, and result in non-linearity and frequency dependence of the piezoelectric response.
Given the important application potential of stable piezoelectrics, uniaxial ferroelectrics and rising interest in FPCs, the present study is focused on evaluating the electromechanical properties of the wurtzite-like structured TEAFBC, which has thus far only been reported from the perspective of its structure and thermodynamic properties [12,13,21,22].The present study provides an improved structural model for TEAFBC using synchrotron-based-single-crystal x-ray diffraction (scXRD) combined with a density functional theory (DFT) study of the elastic compliance, dielectric and piezoelectric coefficients, and an extensive experimental study of the electromechanical response as a function of temperature and electric field frequency and magnitude.

Materials and methods
TEAFBC was prepared by dissolving precursors tetraethylammonium bromide (99 wt%, Sigma Aldrich, USA) and iron(III) trichloride hexahydrate (97 wt%, Sigma Aldrich, USA) in deionized (DI) water.Solution batches were made with a calculated yield of 20 g of crystalline product and formed a total solution volume of 60 ml.The solution was allowed to evaporate at room temperature for seven days after which the solidified crystals were separated from any remaining solution by vacuum filtration and dried in vacuum at 60 • C (supplementary material figure S1).
Density functional theory computations were carried out with the VASP software package using projector augmented planewave method pseudopotentials [28][29][30][31][32].The van der Waals functional vdW-DF-cx was used for the computations as it has previously been demonstrated to generate the smallest absolute deviations from experimentally observed lattice parameters for plastic crystal materials in which the intermolecular bonding is dominated by weak electrostatic and van der Waals bonding [33,34].Elastic and piezoelectric coefficients were obtained using density functional perturbation theory (DFPT) [35,36].The planewave The disordered cell was simplified for DFT computation to avoid using large supercells, due to the significant cost of DFPT computations requiring perturbations of all atoms in the simulation cell.Based on the disordered XRD pattern, we fitted the highest probability structure with mirror symmetry of the second organic cation in the unit cell, to retain the uniaxial polarization of the DFT cell.Furthermore, the structure was simplified to either all Br − , [TEA][FeBr 4 ], or all Cl − , [TEA][FeCl 4 ], see figure 1.
In addition, we performed total energy calculations, with one Cl − atom replaced by Br − , to study the directional its directional dependency.Two structures were studied, one where the Br − atoms are oriented in the direction of the c-axis, and one where the Br − atoms are found in the ab-plane, where the two FeBrCl 3 molecules in the unit cell are oriented in opposite directions.
Electrical measurements were performed on single crystal samples after the surfaces were made parallel by grinding with silicon paper from 2000 to 4000 grade.The expected surface roughness was between 40 and 100 µm.An image of a crystal surface is given in the supplementary material (supplementary figure S1).The sample thicknesses ranged from 0.7 to 0.4 mm.Gold electrodes were sputtered to cover the entire parallel sides of each crystal, thus the total area differed depending on the size of the crystal.The crystal was embedded in a soft gum during deposition to mask the sides of the crystal from electrode deposition.Dielectric spectroscopy was conducted with a thermally controlled Probostat impedance analyzer (Novotherm, Germany) in the frequency range 10 −2 -10 5 Hz using an ac voltage magnitude of 1 V. Direct piezoelectric coefficient was measured using a Berlincourt piezo d 33 meter [37].
Converse piezoelectric measurements, that is electric field driven, were conducted on two different experimental set ups.The high voltage measurements were conducted with the commercially available Tf analyzer (Axiacct, Germany) with a thermally controlled sample stage and a TREK 10 kV signal amplifier and laser interferometer.Two types of measurements were conducted on this apparatus.The first were single cycle bipolar and unipolar hysteresis measurements, where a single trapezoidal voltage signal was applied to the sample and the maximum electric field was increased incrementally with 5 kV cm −1 steps from 0 to 100 kV cm −1 with each successive measurement.The high field piezoelectric coefficient (d 33 * ) was then calculated from the gradient of the linear fit to the resulting displacement vs electric field curves.To determine the frequency dependence of d 33 * under these conditions the electric field maximum was limited to 20 kV cm −1 and the frequency of subsequent loops was varied between 1, 10 and 100 Hz (shown in supplementary materials).The piezoelectric measurements were made with the Tf analyzer CV measurement function using a DC electric field with an overlayed AC small voltage signal.A staircase electric field was used to the DC field with a maximum amplitude of 20 kV cm −1 , while the overlayed small AC signal amplitude and frequency were 2 kV cm −2 and 1000 Hz.For the measurements conducted at different temperatures, the heating stage of the Tf analyzer was used.The temperature was increased from room temperature to 40 • C and then in 20 • C increments until 180 • C. At each temperature the sample was allowed 5 min to equilibrate before the measurements were conducted.Small-signal electromechanical measurements were conducted with a custom-built set up consisting of voltage generator, high-voltage amplifier and fiber optic sensor for strain measurements and lock-in amplifiers to extract small strain signals (for details, see [38].)Differential scanning calorimetry (DSC) measurements were conducted using a DSC 214 Polyma (NETZSCH, Germany) in the temperature range −25 • C to 200 • C. The heating and cooling rate was 10 • C min −1 with a short isothermal hold of 15 min at minimum and maximum temperatures.A total fo three thermal cycles were conducted during each measurement but only the first thermal cycles is presented.A synthetic air atmosphere was used together with closed Al crucibles (NETZSCH, Germany).

Crystal growth
The slow evaporation of aqueous solutions resulted in crystals of TEAFBC with a mixture of different sizes and morphologies.The largest crystals were 5-10 mm long and 5 mm in diameter (supplementary figure S2).The crystals grew with faceted edges and two distinct crystal habits.Trapezoidal prisms resulted when crystals grew with the c-axis oriented in-plane with the bottom surface of the crystallizer (figure 2(a)).Hexagonal prisms formed when the c-axis of the crystal structure was out-of-plane with the bottom surface of the crystallizer (figure 2(b)).The crystals were orientated with the c axis parallel to the length of the clear hexagonal crystal habits, pictured in-plane and out of plane in figures 2(a) and (b) respectively.The polar axis orientation was confirmed with piezoelectric measurements (see later discussion in results and discussion-room temperature electromechanical response).To demonstrate the defining characteristic of the plastic crystal, that is its plastic deformability, a crystal was crushed with a mortar and pestle and then the powder hot pressed together to form a plastically deformed dense body (figure 2(c)).

Crystal structure
The single crystals were evaluated using a synchrotron radiation source at SNBL BM01, ESRF.Diffraction images, collected as the crystal was rotated around a single axis, were compiled into a 3D reciprocal space map of which three orientations are shown in figure 3(a).A structural model of the unit cell was built from the crystallographic information file (cif) that resulted from Rietveld refinements of the diffraction data.The structure reported by Evans et al [13] served as a starting point for the structural refinements.The structural model of the unit cell with comparable orientations to the reciprocal space maps are shown in figure 3(b).
The diffraction data confirms that the TEAFBC crystal was a single-phase material with the hexagonal crystal system and P6 3 mc space group (figure 3(a)i and bi, and table 1).The organic cation sublattice appears to constitute the alternating A and B layers of the hexagonal structure, while the inorganic anions occupy equivalent positions in the sublattice of each layer.When the structure is viewed looking down the a-axis the layers are easily visible (figures 3(aii) and (bii)).Parallel to the c-axis the structure exhibits off centering of the two sublattices and the ethyl chains from the organic molecules in adjacent layers overlap, creating the illusion that the organic molecules are linked (figures 3(aiii) and (ciii)).
The structure exhibits considerable orientational disorder of the organic cations.This is dealt with in the structural model by adopting a nonrigid body approach [39].The structural model allowed five possible atomic sites for each carbon atom, with two fixed distances from the nitrogen atom, c1 and c2, as a soft constraint.The distances were consistent with the bond lengths and angle of the ethyl chains.A distribution of electron density was formed by reducing the occupancy of each carbon position so that the total number of carbon atoms present matched the stoichiometry of the composition.Deviation from stoichiometric occupancy is seen in the chemical formula sum (table 1).Refinement of the anisotropic parameters produced smearing of the carbon positions and a slight asymmetry of the organic cation in the a, c plane.The hydrogen atoms were left out of the model for refinement due to their small mass and thus poor interaction with x-rays.R factors from the fit and other structure information is given in table 1.The cif file produced from the refinement has been validated using CheckCIF and is published with the manuscript.
The anion exhibits tetrahedral coordination of the Fe 3+ by four halide species, one Br − and three Cl − previously thought to be randomly distributed across two symmetry nonequivalent positions (figure 3).The refinement revealed a clear preference of Br − for the position aligned with the c lattice direction with occupancies of 0.33 in the c aligned position and 0.25 in the position of the ab plane.While the percentage of Br − occupancy in the c direction is considered only an approximation, the result clearly shows preferential   3(b) iv, where the larger fraction of green on the halide site parallel to the c axis is circled in red and represents the larger mol fraction of Br − , compared to the smaller mol fractions of Br − found in the a and b plane positions that are circled in blue.The physical justification for this orientation is likely the larger polarizability of the Br − , compared to Cl − , which would result in a lower free energy of the structure when aligned to the polarization field of the crystal parallel to the c-axis.This was in line with the DFT result which found a total energy per [FeBrCl 3 ] − to be 45 meV lower for a unit cell with Br − oriented along the c-axis compared to the case where was Br − aligned with the ab plane (in two different directions).Note however, that this energy should be very sensitive to thermal expansion and disorder.The slow crystallization process, which takes place over a seven-day period, likely allows sufficient kinetic and thermodynamic conditions for the molecular anions to partially orient themselves during the adatom growth at the crystal surface.Some diffuse scattering, evident at several reciprocal space points and most visible in the smearing of points in figure 3(aiii), was thought to be related to the presence of crystal fragments or amorphous layers at the surface of the crystal.In this work, the crystal structure is reported at room temperature only.The mesophase transition is known to occur at 150 • C on heating with large entropy change and hysteresis upon cooling, which together with temperature dependent structural characteristics are reported elsewhere [11].

Computationally determined material parameters
Density functional theory (DFT) investigations of plastic crystal ferroelectrics are of significant interest as they can give insight into the mechanistic origin of the electromechanical coupling [34].Recently, van der Waals exchange-correlation functionals, such as vdW-DF2 and vdW-DF-cx, were shown to provide a higher degree of accuracy compared to conventional solid-state mater functionals, such as PBE, for studying FPCs that are dominated by weak chemical bonding [33,40,41].Here vdW-DF-cx was used both for relaxation and to determine the dielectric, piezoelectric and elastic coefficients using density functional perturbation theory (DFPT).Table 2 presents some key results from the DFT calculations, starting with the unit cell parameters and the free energy, followed by the piezoelectric coefficients (d), the relative permittivity (ε r ) and the elastic compliance (C).
The computed longitudinal piezoelectric coefficient (d 33 ) of 6-8 pm V −1 are larger than that of unmodified AlN, which is 3.4 pm V −1 [14], while the transverse and shear coefficients (d 31 , d 25 ) were smaller and negative (see table 2).The ratio between the shear and longitudinal coefficients (d 16 /d 33 ) is a metric used to evaluate the degree of polarization vector rotation in metal oxides, and can be linked to the amount of molecular rotation occurring in molecular ferroelectrics, that is involved with producing the piezoelectric response [34].In TEAFBC the low values just above 1 were expected due to the uniaxial nature of the P6 3 mc hexagonal structure, further indicating that it is the strain between the relative molecular layers perpendicular to the c axis that results in the change in net polarization.Permittivity values were relatively uniform with crystal lattice direction, and low (∼3.5;table 2) due to the low contributions from the elements in the organic molecules.
The elastic compliance values were anisotropic, with the largest values of around 14 GPa being parallel to the lattice directions and smaller values of 3 or 5 GPa for the diagonals.This was likely a reflection of the intermolecular bond density and distance in the respective directions.These elastic compliance values of TEAFBC fall between the existing piezoelectrics AlN and PVDF which have somewhat comparable dielectric and piezoelectric responses.AlN exhibits elastic compliance values between 98 and 376 GPa, while PVDF has values between 2.5 and 3.5 GPa [42,43].Thus TEAFBC provides intermediate mechanical properties which may prove useful for novel device design.

Room temperature electromechanical response
The electromechanical properties of TEAFBC single crystals were measured systematically with the a, b and then c, axis aligned parallel with the electric field.When the electric field was aligned approximately parallel with the a or b lattice directions the materials exhibited a linear polarization with similar magnitude to the c axis measurements.The strain measurements showed non-linear and irreproducible behavior below the magnitude of ±15 nm regardless of the electric field magnitude (see supplementary materials figure S3).The irreproducibility of the strain behavior together wit hits small magnitude and lack of electric field magnitude dependence indicates that it was related to noise and measurement artifact rather than any distinguishable electromechanical effect of the crystal.Thus, the crystals were deemed to have no piezoelectric response in the a, b lattice direction consistent with that expected from their P6 3 mc crystal symmetry.Since no distinguishable electromechanical response was observed in crystals with the a, b orientation, only the results from c-oriented crystals are discussed further.
The direct piezoelectric coefficient (d 33 ) was first measured for five virgin single crystals, meaning that had experienced no prior electric field, using a Berlincourt tester obtaining values between 5.5 and 7.5 pC N −1 .The variation of d 33 likely arose from variations in the crystal integrity, electrode quality and crystal misalignment caused by polishing.The low fracture strength of the crystals also caused them to crack or chip easily during direct measurements.
Following direct measurements, the strain and polarization behaviors were measured using a high voltage signal with a bipolar sinusoidal waveform.At field amplitudes up to 100 kV cm −1 and frequencies of 100 Hz, the crystals behaved as linear dielectrics, represented by linear polarization-electric field (P-E) (figure 4(a)) and circular current density-electric field (I-E) (figure 4(b)) hysteresis loops.Small anomalies in the I-E loop near maximum fields were related to electric arcing events between electrodes, but generally the crystals exhibited exemplary dielectric properties with small signs of loss, as indicated by the minimal area inside the P-E loops [44][45][46].The maximum polarization was approximately 0.32 µC cm −2 , an order of magnitude or so lower than what is commonly observed during ferroelectric domain switching of switching of many molecular FPCs [5][6][7][8].The P-E loops showed very little hysteresis and a zero remanent polarization (polarization at zero electric field), which is a clear sign that no ferroelectric domains were switched during field application [1].
The strain-electric field (S-E) behavior was measured simultaneously to the P-E and I-E loops (figure 4(c)).The S-E behavior showed an approximately linear strain in both electric field directions with a maximum of approximately 0.007%, typical for a single domain or poled piezoelectric material [1].The deviation from linearity was attributed to measurement artifacts, such as drift and noise, which occurred with a frequency below that of the measurement frequency.The strain behavior showed positive strain (expansion) and negative strain (contraction) in the positive and negative electric field directions, respectively, confirming the approximately parallel alignment of the c-axis of the crystal with the field.When the sample was physically rotated by 180 degrees, so that it was aligned antiparallel to the electric field, the strain behavior was reversed (supplementary figure S4), which is consistent with a piezoelectric response without any ferroelectric domain switching.
As a standard approach, a linear approximation of the strain gradient, indicated by the dashed line in figure 4(c), which corresponds to a ratio of the strain and field amplitudes, was used to calculate the piezoelectric coefficient of the material experienced at electric fields up to 100 kV cm −1 .This high-field piezoelectric coefficient (d 33 * ) was 7.7 pm V −1 .We note the distinction between low and high field d 33 is important due to the potential variation in mechanistic contributions to the strain that can take place as a function of field.However, we note that the high and low field distinction is usually made with respect to the coercive field (E c ), that is the electric field at which domains switch, and in this case the E c is unknown.For the AlN family of thin film hexagonal uniaxial ferroelectrics, the coercive fields are high, up to 4000 kV cm −1 and thus, since they have not been observed, it might be reasonable to speculate that the coercive fields in TEAFBC are far above 100 kV cm −1 .

Piezoelectric coefficient stability
To probe the stability of electromechanical properties of the TEAFBC crystals the converse piezoelectric effect (d 33 ) was studied under alternating current (AC) electric fields with different electric field magnitude, frequency, and DC bias conditions.These measurements were supported by additional dielectric spectroscopy.
The crystals were first stimulated with small AC amplitudes from 0.5 to 2.75 kV cm −1 and signal frequencies from 0.4 to 90 Hz (figure 5(a)).In this entire signal range, the maximum variation of the d 33 from the mean value of 5.6 pm V −1 was 3.4%.In this small field range, there was no clear trend in d 33 variation with increasing field amplitude.The largest variation observed for a single frequency was 1.4%, which occurred at the lowest measured frequency of 0.4 Hz.We note that this could be a result of difficulties in measuring small strain signals (1-5 nm) at quasi-static driving conditions in the presence of intrinsic drift signals related to the fiber-optic light sensors.
Dielectric spectroscopy measurements which varied the AC electric field amplitude between 0.001 and 2 kV cm −1 over a frequency range 10 −1 -10 4 Hz were used to examine the presence of electrical losses in the single crystals.This is of interest as it has been shown in some cases that electrical loss can be linked with electromechanical effects [44][45][46].The measurements showed an increase in the imaginary (out-of-phase) dielectric constant (ε ′′ ) with decreasing frequency from 10 3 to 10 −1 Hz with a minimum in the ε ′′ occurring at 10 3 Hz (figure 5(b)).Additional complex impedance functions, the real permittivity (ε ′ ), real impedance (Y ′ ), and imaginary modulus (M ′′ ), are given in the supplementary information (supplementary figure S5).The dielectric spectroscopy further revealed that in this frequency range the ε ′′ increased with increasing AC voltage amplitude, while at frequencies above 10 3 there was no ε ′′ dispersion with amplitude.This indicated a mechanism of electrical loss susceptible to field amplitude that was frozen out of the response at high frequencies.Mechanisms such as mobile charged defects and dielectric-electrode interfaces effects such as Maxwell-Wagner relaxation or Schottky barriers in single crystals, may produce such an effect [45,46].The deviation observed in the d 33 thus may be linked to these extrinsic effects.
The frequency dependence of the piezoelectric response was greatly increased when the electric field was increased by an order of magnitude to 20 kV cm −1 .For these measurements the S-E loops were measured with single unipolar electric field cycles and the d 33 * was determined from the slope of the average of the strain loop (figure 6).The corresponding S-E loops from which the d 33 * were calculated are provided in the supplementary information (supplementary figure S6).As a function of frequency, d 33 * almost doubled, from 5.8 to 11.3 pm V −1 when frequency was reduced from 100 to 1 Hz.In a multiaxial ferroelectric one might usually assume that the increase of d 33 at low frequencies relates to the increased contribution of domain wall movement, however, in the uniaxial system the contribution from 180 • domain wall movement is expected to be small.Other extrinsic phenomena can also contribute to electric field dependent strain and exhibit frequency dependence, such as the movement of charged defects, however, in the absence of other extrinsic effects we cannot yet rule out kinetics of the intrinsic piezoelectric effect as the cause for frequency dependence.
To further elucidate the effects of electrical field magnitude and leakage on the electromechanical response, the crystals were probed using small AC fields with over-laid DC bias fields (figure 7).First the piezoelectric coefficient was measured with an ac field of 1 kV cm −1 and a DC bias from 0 to 20 kV cm −1 at  different temperatures.The small strain signal led to point-to-point variation of up to 80% associated with instrument noise and small strain signal, so the linear fits of the measured data are reported and show clear trends for each measurement temperature (figure 7(a)).
First, considering the close to room temperature measurement at 40 • C, the variation of the small signal d 33 as a function of DC bias magnitude was only 16%, which was lower than that determined for AC fields of the same magnitude.As a function of temperature, the d 33 variation was 28% between 40 • C and 150 • C and was only 12% over the temperature interval 20 • C-120 • C. Considering both DC bias and temperature parameters together gave a d variation of 38% up to 140 • C and 54% to 150 • C where the solid-to-mesophase transition begins.Generally, it was observed that the d 33 remained stable to 80 • C before it began to decrease and finally became more unstable with bias field at 150 • C. We propose that the origin of this is extrinsic in nature, that is, it is related to increase electrical loss and potential charge defect migration causing heterogeneous local electric fields and decreased displacement, as opposed to intrinsic effects associated with the crystal lattice itself, such as softening of the elastic compliance coefficient.By comparison the hybrid perovskite (CH 3 ) 3 NCH 2 ClMnCl 3 shows a small increase in its piezoelectric coefficient between room temperature and the depolarizing curie transition at approximately 120 • C [11].Such behavior is more likely related to intrinsic effects, such as softening of the crystal lattice with temperature allowing for more displacement, while the electrical losses remain low.The proposed explanation for d 33 temperature dependence observed with TEAFBC is supported by the loss and temperature dependent high field measurements presented below as well as by the dielectric loss studies presented in an earlier manuscript by Walker et al [12].Increased electrical losses will reduce the effective electric field seen locally by the lattice and thus reduce the piezoelectric response correspondingly as well as produce charge distributions which may produce further heterogeneities in the electric field distribution [47].
When DC biases with different directions were considered, the d 33 was seen to decrease with a positive DC bias and increase with a negative bias.This effect might be explained by dielectric stiffening of the crystal [48,49].In ferroelectrics the dielectric response is known to diminish under a positive DC bias, parallel with the average polarization vector, and increase with a negative DC bias, anti-parallel with the polarization.The dielectric response reaches a maximum at approximately the coercive field for ferroelectric domain switching.As there is no ferroelectric domain switching observed for the TEAFBC the behavior is akin to that occurring below the coercive field.The relationship between the dielectric constant of the material and its piezoelectric coefficient may thus be explained approximately through a classical mechanics model [50].
By studying the dielectric response under the same DC bias field conditions, possible extrinsic origins for the effect are also visible [46].The ε ′′ under positive DC bias shows little dispersion as a function of frequency, having a local minimum around 500 Hz and rising steadily with the electrical loss below this minimum (figure 7(b)).The ε ′ , Y ′ and M ′′ complex impedance functions correlating with this data are given in supplementary information (supplementary figure S7).The ε ′′ signal under a negative DC bias on the other hand reveals a significant dispersion that occurs below 100 Hz (figure 7(c)).Similarly, the ε ′ , Y ′ and M ′′ complex impedance functions correlating with this data are also given in supplementary information (supplementary figure S8).The ε ′′ values in the low frequency region are largest at the largest negative DC bias field, and these approximately match those recorded under positive DC bias for the same frequencies.So, at low DC bias fields in the negative direction the crystals experience a dielectric relaxation in the ε ′′ that was removed by increasing the magnitude of the bias field.
The different dielectric loss behavior as a function of bias field direction is important as it gives information about the possible extrinsic and intrinsic mechanisms that may contribute to the electrical response.In metal oxide single crystals such behavior often indicates the influence of an extrinsic mechanism, commonly a non-rectifying electrode interface [46].However, these ionic plastic crystals are less well understood, and it is not yet known if there are additional intrinsic mechanisms that might cause nonlinear electrical responses.For example, the weak electrostatic bonding present in ionic plastic crystals, or the rotation under electric field of polar molecules like [FeBrCl 3 ] −1 , may cause additional intrinsic contributions to electrical and electromechanical nonlinearity.This hypothesis is supported by the known contribution of molecular rotation to the shear piezoelectric coefficients in ionic plastic crystals [34].Thus, we cannot yet exclude the possibility of either an electrode interface effect or mechanisms intrinsic to the crystal lattice as contributing to the DC bias effect observed.

Temperature dependent electromechanical response
Before we present the temperature dependent electromechanical behavior in detail it is necessary to discuss the phase transition behavior in the TEAFBC single crystals.DSC curves clearly show the onset of the P63mc to mesophase Pm-3m phase at 150 • C in both powder and single crystals samples (figure 8).The peaks on cooling take place very abruptly at 105 • C demonstrating hysteresis of 45 • C. the insets in figure 8 show the heating and cooling transitions in detail and it is observed distinctly that the single crystal curves exhibit lower intensity and broader peaks.On heating the single crystal transition is not completed until approximately 167 • C compared to the powder which is complete near 162 • C. The slower kinetics of the polymorphic transition in the single crystal were most likely due to the heterogenous nucleation of the Pm-3m mesophase taking please preferentially at the surfaces and interfaces.As the powdered sample had a greater surface area to volume ratio the transition was able to progress to completion faster.
The temperature-dependence of the electromechanical response was further assessed by high voltage measurements at 50 kV cm −1 and 100 Hz with a sinusoidal wave form, made at 20 • C intervals between 40 and 160 • C. No data was collected above 160 • C due to the crystals experiencing dielectric breakdown.The dielectric response remained very consistent up to 100 • C with only minor increases in the electrical losses, related to increases in the electrical conductivity, which was visible in the P-E and I-E hysteresis loops by the fact that the loop shapes remained consistent (figures 9(a) and (b)).At 120 and 140 • C the I-E loops distinctly rotated anticlockwise, an indication that the current signal was shifting out of phase with the applied electric field, as is expected with increases in the electrical conductivity.Correspondingly, the P-E loops became more oval shape and the area inside the loop increased, indicating greater electrical loss [45,46].At 160 • C the P-E loop exhibited a massive increase in electric loss, indicated by the circular-type shape (red loop in figure 9(a)).The I-E loop shape also exhibits a clear nonlinear character with enhanced current amplitudes giving it a divergent-like shape, exhibiting sharp peaks at the maximum electric fields (red curve in figure 9(b)).This type of current behavior is close to that exhibited by a semiconductor or high loss dielectric [45,46].The roughened line of the loop in the first quadrant of the field cycle was related to arcing events.Marked by a black arrow in figures 9(b)) and (d).From the literature we know the material undergoes a phase transition from solid to mesophase at 150 • C and that the electrical conductivity significantly increases at this transition [12].In the mesophase both the organic and inorganic molecular constituents  exhibit degrees of orientational freedom, consistent with a plastic crystal material behavior.High conductivity is widely observed in the mesophase state of plastic crystals and is attributed to the high ionic mobility facilitated by the orientational freedom of the molecules, suggesting that the behavior observed in figure 9 is nonlinear (non-Ohmic) conductivity [51,52].This is consistent with the introduction of semiconductor like behavior in the I-E and P-E loops at 160 • C.
The strain behavior as a function of temperature is valuable to study as it does not show the same direct contributions from electrical conductivity as the current density and polarization.The crystal displacement was on the order of approximately 50 nm, with a noise floor of approximately 5 nm in the instrument, and thus drift was considered responsible for irregularities in the data.The strain behavior exhibited up to 160 • C was consistent with an approximately linear piezoelectric response even at the temperatures where the electrical loss was highest (figure 9(c)).This is consistent with the small signal d 33 measured as a function of temperature (figure 9(a)) which also showed the piezoelectric response still present at 150 • C.However, the high-field strain response measured here does not show any distinguishable trend as function of temperature which indicates good temperature stability despite increased electrical loss.
The coexistence of piezoelectric strain and high conductivity near the phase transition is intriguing as it suggests that at the phase transition temperature (150 • C) there is an overlap in the properties of the low and high temperature phases, the piezoelectric response of the low temperature P6 3 mc phases and the high conductivity of the Pm-3m mesophase [12].To show this behavior more clearly, we have plotted the current density (figure 9(d)) and the strain (figure 9(e)) as a function of time for the key temperatures 40, 120 and 160 • C where changes in behavior were observed.The current density was seen to transition from approximately 90 • out of phase with the electric field, as expected for a dielectric, to almost completely in phase, as expected for a conductor.The strain behavior remains more consistently in phase with the electric field, but the phase is difficult to quantify due to the signal noise.It does however, appear as though the strain goes from having a slightly positive phase angle (delayed from the electric field) to having a slightly negative phase angle (time-advancing the electric field) at 160 • C. Negative electromechanical phase angles are usually (but not always) explained by the extrinsic effects of Maxwell-Wagner type relaxation caused by electrical heterogeneities (local regions in the material with different magnitudes of the electrical conductivity) [47,53].
Impedance spectroscopy as a function of temperature was carried out to examine the loss behavior of the material more thoroughly (figure 10).However, we note that this was conducted on polycrystalline sample to look more specifically at bulk loss behavior without electrode-crystal interface effects.The ε ′′ behavior showed both a steady increase with reducing frequencies between 10 5 and 10 −1 Hz and as the temperature was increased between 25 • C and 180 • C (figure 10(a)).With the ε ′′ increasing three orders of magnitude in this temperature range.A clear anomaly in the vicinity of 150 • C is indicative of the known mesophase transition.The real admittance (Y ′ ) shows a similar increase for frequencies and temperature.Interestingly the admittance as a function of temperature converges towards the mesophase transitions, coming together at 130 • C and then exhibiting an anomalous hump between 150 • C and 160 • C. Both ε ′′ and Y ′ show an increasing electrical loss or and conductivity behavior as the temperature increases up to the phase transition, supporting the high field electromechanical data of figure 9.The fact that the anomalies at the transition do not demonstrate as severe an increase in electrical conductivity as see in figure 9 during the high field measurements indicates that there may be significant contributions to the electrical loss from non-ohmic and thus field magnitude dependent mechanisms.Such mechanisms may be electron hoping, vacancy migration and point defect conduction.
Meanwhile, at temperatures below room temperatures we expect the piezoelectric response to remain stable until the first polymorphic phase transitions at −43 • C to a twinned P6 3 [21].The uniaxial polarization of the P6 3 mc phase without ferroelastic domains suggests that the piezoelectric response is dominated by intrinsic lattice contributions which should not change too much before the transition.Further supporting this are our piezoelectric coefficients computed with DFT, with shows close correlation with experimental results and represent an intrinsic lattice response.The P6 3 is a twinned polar structure and thus maybe expected to exhibit a piezoelectric response.The second transition near −100 • C is known to change the structure to an orthorhombic Pca2 1 space group, which is also polar but we have no data on what the piezoelectric response might be.

Summary and conclusions
With this work we have studied in depth the electrical and electromechanical response of uniaxial ionic plastic crystal single crystals [(C 2 H 5 ) 4 N][FeBrCl 3 ].The single crystals have a hexagonal P6 3 mc crystal structure and exhibit an orientational preference of the Br − halide species parallel with the polarization direction in the crystal.The electromechanical response under high bipolar electric field indicated a clear piezoelectric response, with d 33 * of 7.7 pm V −1 , without influence from ferroelastic domains, in agreement with crystal-symmetry arguments.The electromechanical response persisted with similar magnitude right up to the phase transition temperature at 150 • C. A series of piezoelectric measurements as function of AC field magnitude and frequency showed that the crystals exhibited high piezoelectric stability, varying by only 3.4% with both stimuli.As a function of DC bias the d 33 varied by 16% and by 12% as a function of temperature up to 120 • C. At temperatures above this the d 33 deteriorated significantly but due to the strain signal that was still observed up to 160 • C it is likely the d 33 variation is due to high leakage currents rather than depolarization.[(C 2 H 5 ) 4 N][FeBrCl 3 ] crystals thus show promising properties for small ac signal applications and in a moderate temperature range up 120 • C. While leakage currents and interface effects, especially at elevated temperatures, are challenges that need to be addressed in the future, the soft mechanical properties combined with the piezoelectric response put this FPC in a parameter space separate from existing wurtzite piezoelectrics and may yet find niche application.

Figure 2 .
Figure 2. Single crystals grown as (a) trapezoidal prisms with c axis in-plane, (b) hexagonal prisms with c axis out-of-plane with respect to the crystallize bottom.(c) A crystal that has been crushed and then hot pressed together at 180 • C.

Figure 3 .
Figure 3. (a) 3D reciprocal space map constructed from single crystal diffraction data, oriented (i) standard unit cell configuration, (ii) parallel to a axis, (iii) parallel to c axis.(b) 3D structural models built from refined crystal structure with orientation corresponding to i, ii and iii reciprocal space maps.(iv) shows a single [FeBrCl3] molecule with the halide site parallel to the c axis circled in red identifying the site with a 0.33 mole fraction of Br − .Blue circles show the sites with a 0.25 mole fractions of Br.

Figure 4 .
Figure 4. (a) polarization, (b) current density, and (c) strain as a function of electric field for single crystals with the c axis parallel to the field direction.Electric field amplitude of 100 kV cm −1 and a frequency of 100 Hz were used.Dashed line in (c) is a guide to the eye marking the linear average used to calculate d33 * .

Figure 5 .
Figure 5. (a) Converse piezoelectric coefficients measured as a function of small AC electric field amplitude (<3 kV cm −1 ) and frequencies from 0.4 to 90 Hz.(b) Imaginary part of the dielectric constant (ε ′′ ) as a function of frequency and AC electric field amplitude <2.0 kV cm −1 .

Figure 6 .
Figure 6.Piezoelectric coefficients measured (a) as a function frequency (with a log scale) at high electric field (20 kV cm −1 ).

Figure 7 .
Figure 7. (a) Linear fits of the piezoelectric coefficients measured as a function of DC bias electric field and measured at different temperatures between 40 and 150 • C. (b) and (c) imaginary dielectric constant as a function of frequency at DC bias fields 0-20 kV cm −1 for (c) positive and d) negative bias field directions.

Figure 8 .
Figure 8. Differential scanning calorimetry heat flow (mW mg −1 ) as a function temperature for single crystal and powder samples of TEAFBC.Inset (i) and (ii) show closeups of the phase transition peaks on heating (endothermic) and cooling (exothermic) respectively.Red dashed lines mark the transition temperatures, dashed boxes mark the region of the insets.Horizontal arrows mark the heating and cooling directions and vertical arrows mark the endo-and exothermic directions.

Figure 9 .
Figure 9. (a) Polarization, (b) current density and (c) strain as a function of electric field at temperatures from 40 • C to 160 • C for single crystals with the c axis parallel to the field direction.Electric field amplitude of 50 kV cm −1 and a frequency of 100 Hz. in (c) measurements at temperatures 40, 120 and 160 • C are plotted in thick lines while others are in thin lines to make the plot easier to read.The arrows in figures (b) and (d) mark the region of the current loop where arcing was identified.

Figure 10 .
Figure 10.Dielectric impedance spectroscopy data represented as the complex impedance functions of imaginary permittivity (a) ε ′′ and real admittance (b) Y ′ for TEAFBC polycrystalline samples, measured as a function of temperature between 25 • C and 180 • C.

Table 1 .
Crystal data and structural refinement parameters for TEAFBC single crystal diffraction.

Table 2 .
Key parameters from density functional theory calculations.