Progressive Structural Complexity in Ferroelectric 1,2,4-Triazolium Hexabromoantimonate(III): Interplay of “Order–Disorder” and “Displacive” Contributions to the Structural Phase Transitions

Halobismuthates(III) and haloantimonates(III) with the R3MX6 chemical composition create a new and broadly unexplored class of ferroelectric compounds. In this paper, we report the haloantimonate(III) ferroelectric comprising an aromatic (1,2,4-triazolium) cation, i.e., (C2N3H4)3[SbBr6] (TBA). Temperature-resolved structural and spectroscopic studies indicate that TBA undergoes two solid–solid phase transitions between tetragonal [P42/m (I)] and monoclinic [P21/n (II) and P21 (III)] phases. TBA experiences a paraelectric–ferroelectric phase transition at 271/268 K (II–III) driven by “order–disorder” and “displacive” molecular mechanisms. The ferroelectric properties of phase III have been confirmed by hysteresis loop measurement, and additionally, the acentric order has been further supported by second-harmonic generation measurements. Insight into the molecular origins of the ferroelectric polarization was provided by periodic ab initio calculations using the Berry phase approach at the density functional theory (DFT-D3) method level employed for calculations of spontaneous polarization.


Table of contents:
Section 1: Experimental description Section 2: PXRD Figure S1. The X-ray diffraction pattern at 298 K of TBA (red) and calculated from crystal structure (blue). Section 3: Thermal properties Figure S2. Simultaneous thermogravimetric (TGA) and differential thermal analyses (DTA) scan (ramp rate: 5 K min −1 ). Figure S3. DSC traces for TBA during the cooling and heating scans (rate: 5 K·min -1 , sample mass 13.1430 mg). Section 4: Crystal structure analysis Table S1. Crystal data and abbreviated information about structure refinement results and periodic ab initio calculated data for TBA. Table S2. The geometry of [SbBr6] 3units ( a -X-ray, bcalc.) bonds in [Å]; angles in [deg] Table S3. The geometry of hydrogen bonds in TBA at 100 K ( a -X-ray, bcalc.) bonds in [Å]; angles in [deg] Figure S4. The TBA packing in the tetragonal phase (crystallographically unrelated cations A and B are distinguished by blue (A) and red (B) color). Figure S5. The symmetry and the orientation of the unit cell of the tetragonal, monoclinic centrosymmetric and monoclinic polar phases of TBA. Figure S6. Comparison of TBA packing at 320 (left), 293 (center) and 100 K (right). Figure S7. The scheme of the short (green) and the long (orange) Sb-Br bond in TBA at (a) 293 K (b) 100 K and the orientation of the dipole moment of the cations (c) at 100 K with anions presented as octahedra. The [Sb(3)Br6] 3octahedra are distinguished by green color. Figure S8.  Figure S11. The frequency dependence of (a) the real and (b) the imaginary part of permittivity at several temperatures. Figure S12. The dependence of '' versus ' for the single crystal of the TBA complex. The solid line represents fit to the Cole-Cole equation. Figure S13. Temperature dependence of the macroscopic (τ ) and microscopic (τ0) relaxation time and its inverse (τ0 −1 ) above Tc.

Thermal analysis
DSC measurements were performed by heating and cooling of the polycrystalline sample in the temperature range of 100-320 K with a ramp rate of 5 K•min −1 using a Metler Toledo DSC 3 instrument. The TGA/DSC measurements were performed on a TGA-DSC 3+ instrument between 290 and 740 K with a ramp rate of 5 K min −1 . The scan was performed in flowing nitrogen (flow rate: 1 dm 3 h −1 ).

Crystal structure determination
The X-ray data of TBA were collected at 320 K, 293 K and 100 K using an Oxford Cryosystem device. X-ray data were collected on a Xcalibur Sapphire2 diffractometer (MoK radiation;  = 0.71073 Å). Data reduction and analysis were carried out with the CrysAlis 'RED' program. 1 Space groups were determined, based on systematic absences and intensity statistics. Structures were solved by Patterson method using the SHELXS program and refined using all F 2 data, as implemented by the SHELXL programs. 2 Positions of carbon and nitrogen atoms in triazolium cations were chosen on the base of distances to potential Br and N acceptors of hydrogen bonds. In TBA at 293 K and at 320 K most of triazolium cations are disordered and the C/N arrangement in the disordered triazolium rings is unreliable. Non-hydrogen atoms were refined with anisotropic displacement parameters. However, in the structure at 293 K and at 320 K, the geometry of the disordered triazole rings and displacement parameters of their atoms were restrained using AFIX and ISOR commands, respectively. Moreover, for partially overlapping atoms, SIMU restrain was applied. At 293 K, occupancy factor of the disordered triazole rings were refined assuming that the sum of all components of a given disordered cation located in general and in the special positions is equal to 1 and 0.5, respectively. In the crystal structure at 293 K and at 320 K, H atoms were not found. At 100 K, all H atoms were found in  map, and before the last refinement cycle, they were fixed and were allowed to ride on their parent atoms.

Electric properties
Electrical measurements of TBA were performed on polycrystalline samples in the form of pressed pellets with geometrical parameters (S = 20-25 mm 2 , d = 0.8-0.4 mm). The complex dielectric permittivity was measured between 250 and 320 K by an Agilent E4980A Precision LCR Meter in the frequency range of 135 Hz-2 MHz. The electric measurements were carried out in a controlled nitrogen atmosphere. The overall error for the complex permittivity real and imaginary parts was less than 5%. The ferroelectric hysteresis loops were obtained by using a Sawyer-Tower circuit Precision Premier II (Radiant Technologies, Inc.) at a frequency of 50 Hz. The surfaces of the pellet were coated with a gold electrode with a mask using a sputter coating system (Quorum Q150T S).

Second harmonic generation (SHG)
Temperature-resolved SHG studies were performed using a laser system employing a wavelengthtunable Topaz Prime Vis-NIR optical parametric amplifier (OPA) pumped by Coherent Astrella Ti: Sapphire regenerative amplifier providing femtosecond laser pulses (800 nm, 75 fs) at 1 kHz repetition rate. The output of OPA was set to 1300 nm and was used unfocused. Laser fluence at samples was equal to 0.25 mJ/cm 2 . The single crystals of TBA were crushed with a spatula and sieved through an Aldrich mini-sieve set, collecting a microcrystal size fraction of 125-177 μm. Next, size-graded samples were fixed in-between microscope glass slides to form tightly packed layers, sealed, and mounted to the horizontally aligned sample holder. No refractive index matching oil was used. The employed measurement setup operates in the reflection mode. Specifically, the laser beam delivered from OPA was directed onto the sample at 45 degrees to its surface. Emission collecting optics consisted of a Ø25.0 mm plano-convex lens of focal length 25.4 mm mounted to the 400 μm 0.22 NA glass optical fiber and was placed along the normal to the sample surface. The distance between the collection lens and the sample was equal to 30 mm. The spectra of the nonlinear optical responses were recorded by an Ocean Optics Flame T fibercoupled CCD spectrograph with a 200 μm entrance slit. Scattered pumping radiation was suppressed with the use of a Thorlabs 750 nm short-pass dielectric filter (FESH0750). Temperature control of the sample was performed using a Linkam LTS420 Heating/Freezing Stage. Temperature stability was equal to 0.1 K.

Computational Methods (Periodic Ab Initio Calculations)
Quantum-mechanical condensed matter simulations including: a series of full geometry and cell parameters optimizations, spontaneous polarisation (Ps), electronic band structure (EBS) of crystal, the band gap, and density of states (DOS) calculations were performed to localize the key stationary points on the potential energy surface (PES) of the TBA. These calculations employed the London-type empirical correction in the (D3) variant for dispersion interactions as proposed by Grimme 3-6 including three-body dispersion contributions with fast analytical gradients together with the vibrational harmonic frequency calculations. The structural data (starting geometry) were taken from the X-ray crystal structure of TBA from this present study. Calculations were performed using the CRYSTAL17 software, 7,8 utilizing the DFT-D3 3-6 methods with the hybrid functional: the Becke's three-parameter functional combined with the nonlocal correlation Lee-Yang-Parr (B3LYP-D3) 9-11 with the two shrinking factors (4',4') to generate a commensurate grid of k-points in reciprocal space, following the Monkhorst-Pack 12 net method. All calculations were carried out with the consistent gaussian basis sets of double zeta valence with polarization quality for solid-state calculations (pob_DZVP_rev2) in second revision include BSSE-correction scheme as proposed by Peintinger, Vilela Oliveira, Laun and Bredow [13][14][15][16] . For the antimony atom we have used for the calculation Sb_pob_DZVP_2018 basis set 15 which is an extension of the pob_DZVP basis set, and is based on the full-relativistic effective core potentials (ECPs) of the Stuttgart/Cologne group and on the def2-SVP valence basis 16,17 of the Ahlrichs group. To check if the crystal structure of TBA is at the global minimum on the PES after optimization, IR harmonic frequencies were calculated. The imaginary frequencies were not found. For the TBA crystal, vibrational frequency calculations using CRYSTAL17 were performed at the Γ-point 18,19 . The spontaneous polarisation (Ps) in the TBA crystal was calculated and evaluated through either a Berry phase (BP) approach 20-22 as the polarization difference between one of the two enantiomorphic structures (λ=+1 or λ=−1) and the intermediate geometric structure (λ=0). The electronic band structure was generated according to the procedure in the CRYSTAL17 program. In order to prepare the input file, the SeeK-path 23 tool was also used, and the EBS and DOS were visualized in CRYSPLOT 24 and Gnuplot 25 programs.

UV-vis spectroscopy
The diffuse reflectance and absorption UV-vis spectra at room temperature were recorded with Cary 5000 spectrophotometer.