Lattice Dynamics in Organic Ferroelectrics Using Neutron Spectroscopy and Ab-Initio Modeling

Lattice dynamics in organic ferroelectric PhMDA (2-phenylmalondialdehyde C9H8O2) has been investigated using inelastic neutron scattering (INS) spectroscopy and first principles based calculations. Most of the prominent features of the INS spectrum originated from the normal modes of hydrogen bonded malondialdehyde (MDA) units rather than from phenyl rings. It is also found that carbon-hydrogen bonds in the MDA unit are tighter than these in phenyl rings. From the calculated splitting of LO (longitudinal optical) and TO (transverse optical) normal modes, it is predicted that hydrogen bonds in MDA units, which hold the solid state structure, contribute more to the ferroelectric polarisation of PhMDA. Any distortion of H-ions in these hydrogen bonds thus affects ferroelectric properties of this material.

although this is important to understand ferroelectric properties of materials. In the current article, we present experimental vibrational spectra of PhMDA using INS spectroscopy and microscopic lattice dynamics analysis employing first principles DFT calculations to understand the atomistic origin of its ferroelectric polarisations.

Experiments
INS experiments are performed on TOSCA [14] spectrometer at the ISIS Pulsed Neutron and Muon Source at 10 K [15]. About 2.4 g of commercially available PhMDA powder bought from Sigma Aldrich is used in this experiment. TOSCA is a high resolution time-of-flight, indirect geometry spectrometer having energy resolution ΔE/E less than 1% with energy transfer range up to 8,000 cm −1 . The sample is wrapped in a thin aluminum foil and placed in a flat aluminum container sealed by indium wire under vacuum.

Calculations
Calculations are performed using plane wave pseudo-potential electronic-structure calculations as implemented in the CASTEP code [16] with optimized norm-conserving pseudopotentials [17] generated with the Perdew-Burke-Ernzerhof (PBE) [18] functional within the generalized-gradient approximation (GGA). Dispersion corrections are included in the PBE functional (PBE + D) as proposed by Tkatchenko and Scheffler (TS) [19]. The initial atomic structure is taken from the reported experimental structure obtained from XRD measurements and available in Cambridge Crystallographic data center (CCDC) as entry number 796168 [4]. Fullgeometry optimizations using both PBE and PBE + D functionals with a force tolerance of 1.0 × 10 −3 eV/Å are performed with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. A plane-wave cutoff of 1,000 eV and a Brillouin-zone (BZ) sampling of 8 × 2 × 8 k-points equivalent to 16 points when symmetry-reduced are used with selfconsistent single-point energy minimizations tolerance of 2.5 × 10 -7 eV. The tolerance of atomic forces minimization is 1.0 × 10 -3 eV/Å.
Normal mode frequencies and eigenvectors are determined by lattice dynamics calculations at the Γ-point of the resulting ground state structure by diagonalisation of dynamical matrices using the density-functional perturbation theory (DFPT) and linear-response methods [20]. INS spectra are obtained from calculated eigenenergies and eigenvectors and using the abINS algorithm in Mantid [21].
Intensity of a particular INS mode is related to the dynamic structure factor S (Q, E). For a crystal containing N atoms in the unit cell, the structure factor of single-quantum excitation of normal mode m with energy E m at temperature T [24] is: where, e i,m is the eigenvector of atom i in mode m, Q is the momentum-transfer vector, M i is the mass of atom i and W (Q, T) is the Debye-Waller (DW) factor at temperature T. At very low temperatures, the DW term is approximated as zero. For an inverted-geometry INS spectrometer like TOSCA, Q 2 is proportional to E. A powder averaging has been applied in this calculation following standard methodology [21][22][23].

RESULTS AND DISCUSSIONS
The unit cell of PhMDA consists of four molecular units as shown in Figure 1. In each unit a malondialdehyde (MDA) molecule is attached with a six-member phenyl-ring through C=C bond.
Single crystal X-ray diffraction (XRD) found the crystal structure as orthorhombic having space group Pna2 1 , space group number 33 [4]. The phenyl-ring molecular units are connected by hydrogen bonding in a zig-zag manner through MDA units to make the solid state structure. The a and b -lattice parameters obtained for the ground state geometry by cell optimised PBE + D calculations compared within 1%. The calculated c-lattice parameter, however, underestimated by 2.6%. This difference primarily comes from the differences in of lengths hydroxyl and hydrogen bonds. The positions of H obtained from X-ray diffraction may have contributed in this discrepancy. Due to larger differences, 7.8%, 13.2% and 3.8% for a, b and c lattice parameters, respectively, when the unit cell is optimised without Lattice dynamics calculations show that there are 225 optic modes in four different symmetries, A1, A2, B1 and B2. All these modes are Raman-active, however, modes with A1, B1, B2 symmetry only are IR-active. All 57 modes with A2 symmetry are IR-inactive. As there is no selection rule, INS spectroscopy is capable of giving almost complete information of normal modes in this material.
The experimentally obtained INS spectrum is compared with the DFT simulated one in Figure 2. Frequencies of important normal modes and molecular unites responsible for these vibrations are labeled in this figure. Both spectra agree relatively well showing that the calculations using DFT within harmonic approximation can explain almost all vibrational transitions. Although INS experiments are done on powdered sample and DFT calculations are done on a periodic structure, which resembles with the single crystal structure of the material, this agreement shows that the powdered sample retains its local and medium range order of atomic arrangements. The long range order of the atomic structure may be affected more in the powdered sample reflecting the differences between experimental and simulated INS in the low energy modes of collective vibrations.
The vibrational peaks below 400 cm −1 are collective vibrations and dominated by oxygens in MDA units. The sharp peak around 400 cm −1 , labeled as A is Figure 2, is due to a wagging motion of two dangling hydrogens in MDA units, which are not hydrogenbonded. In practice there are four modes ranging between 400, −, 417 cm −1 due to the C-C=C bending modes in MDA. These IR-active modes are clearly visible in INS spectroscopy because these are associated with the motion of hydrogens. However, calculations show that these low energy modes are of low intensities, so may be not be visible in IR spectrum.
The next most intense peaks observed in the INS spectrum are located at 924 cm −1 and 972 cm −1 , labeled as B1 and B2 in Figure 2. These are antisymmetric librational modes of non-hydrogen bonded hydrogens in MDA and the wagging motion of the phenyl-ring and its associated hydrogen atoms, respectively. Corresponding calculated modes are within 1.5% of that of experimental frequencies. Calculations show that these IR-active modes also may not be visible in the IR spectrum due to their low intensities.
The out-of plane bending motion of O-H-O hydrogen bond in MDA chains, observed at 1,151 cm −1 are of relatively lower intensities than the wagging modes at 972 cm −1 mentioned above. This peak is denoted at C in Figure 2. These modes are observed in other hydrogen bonded ferroelectrics, such as croconic acid [8,11] and CBDC [12], around 1,000 − 1,100 cm −1 . The relative INS intensities of these modes are increasingly stronger from CBDC to PhMDA to croconic acid. The vibration of hydrogen bonds in MDA chain along with wagging motion of dangling hydroxyl ions associated with MDA units is observed around 1,230 cm −1 . This peak appears just above the peak denoted as C.
The O-H stretching modes around 2,200 cm −1 , marked as D in Figure 2, are not visible in the INS spectrum. These modes can be visible in IR spectrum due to their moderately high intensities. The clearly visible modes in INS around 3,100 cm −1 , marked as E 2 in Figure 2, are C-H stretching modes associated with phenyl rings in the PhMDA crystal. The C-H stretching modes related with MDA are observed in a little bit lower energy transfer region, i.e., around 2,800 cm −1 , which is labeled as E 1 in Figure 2. This predicts that C-H bonds in MDA unit are tighter than these are in phenyl rings. These C-H stretching modes may not be visible in IR spectroscopy due to their very low intensities as obtained from lattice dynamics simulations.
Lattice dynamics plays an important role in understanding the particular vibrational mode or modes responsible for ferroelectric properties in materials. The LO-TO splitting of normal modes is a measure of their contribution to the dynamical effective charge responsible for ferroelectricity [6,7]. In PhMDA it is found that OH stretching modes around 2,200 cm −1 exhibit LO-TO splitting of about 100 cm −1 . Although this is not huge in comparison to the giant LO-TO splitting of about 700 cm −1 found in inorganic ferroelectric BaTiO 3 [6], this is the maximum LO-TO splitting obtained from calculations. The LO-TO-splitting for the mode at 1,230 cm −1 is about 50 cm −1 . On the other hand, the LO-TO splitting for C-H stretching modes (E 1 and E 2 ) and O-H-O bending mode (C) are negligible.
A comparatively large LO-TO splitting of modes around 2,200 cm −1 , which is associated with hydrogen bonded MDA chain, indicates that these modes couple strongly with electric fields and contribute more to the dynamical effective charge responsible for ferroelectric polarisation. Any distortion of the H-ion in the hydrogen bond as well as hydroxyl ions in MDA