Calculation Of The Damping Constant (FWHM), The Relaxation Time, And The Activation Energy As A Function Of Temperature For DmaCd(N3)3

Abstract

• Raman and IR frequencies are calculated from the molecular field theory for DMACd(N 3 ) 3 . • Raman and IR frequencies were associated with the order parameter. • The relaxation time and the activation energy were calculated for DMACd(N 3 ) 3 . • PS and EF models used for the analysis of IR and Raman active modes were adequate to describe the experimental behavior of the wavenumber and FWHM for DMACd(N 3 ) 3 The Raman frequencies of τ(CH 3 ), υ s (CNC), υ 1 (N 3 ) and δ(CH 3 ) modes, the IR frequencies of δ(NH 2 ) and ρ(NH 2 ) modes, and the corresponding FWHM values for these modes in DMACd(N 3 ) 3 were analyzed by using the experimental data from the literature for both ferroelastic and paraelastic phases. In these analyses, the Raman and the IR frequencies of these modes were associated with the order parameter calculated from the molecular field theory with regard to the structural phase transition (Tc=174 K) in DMACd(N 3 ) 3 , the frequencies and the damping constants of τ(CH 3 ), υ s (CNC), υ 1 (N 3 ), δ(CH 3 ), δ(NH 2 ), and ρ(NH 2 ) modes as a function of temperature through the model of pseudospin (dynamic disorder of DMA + cations and partially N 3 anion), phonon coupling (PS) model, and the energy fluctuation (EF) model by analyzing the experimental data for the frequencies and FWHM of these modes in hybrid organic-inorganic perovskite. Moreover, the relaxation time and the activation energy were calculated for all these modes at various temperatures by using the damping constants (FWHM) for the PS and EF models studied in DMACd(N 3 ) 3 . The results of the present research showed that the calculated Raman and IR frequencies with the damping constants of τ(CH 3 ), υ s (CNC), υ 1 (N 3 ), δ(CH 3 ), δ(NH 2 ), and ρ(NH 2 ) modes adequately accounted for the experimental data in DMACd(N 3 ) 3 . The calculated activation energies for these modes were found to be acceptable compared to the values available in the literature and the k B T c values at the critical temperature. This method for calculating the frequencies (IR and Raman) and FWHM of these modes that were associated with the phase transitions could also be applied to some other hybrid organic-inorganic perovskites.