Temperature dependence of the bandwidths and frequencies of some anthracene phonons. High-resolution Raman measurements

Using a coupled interferometer—spectrometer with a resolution of 0.02 cm^?1 we have measured the Raman band profiles of the four low-frequency anthracene phonons ω₁(a_g), ω₂(a_g), ω₆(b_g) and ω₇(b_g) in the temperature range 2–70 K. These phonons possess very narrow bandwidth at low temperature which are convinently measured under high resolution. In particular the two lowest-frequency phonons ω₁(a_g) and ω₆(b_g) have a bandwidth at 2 K of 0.045 cm^?1. The other two phonons ω₇(b_g) and ω₂(a_g) have bandwidths at 2 K of 0.165 and 0.4 cm^?1, respectively. A detailed analysis of the bandwidth variation with temperature was made in terms of three-phonon decay processes. The exrerimental variation of the bandwidth with temperature was correctly reproduced assuming a single down-and up-process. The following results were obtained: ω₁(a_g): 49.45 cm^?1 = 2×24.72 cm^?1, 49.45 cm^?1 = 98.45 cm^?1 ?49.0 cm^?1; ω₆(b_g): 57.50 cm^?1 = 2×28.75 cm^?1, 57.50 cm^?1 = 108.50 cm^?1 ?51.0 cm^?1; ω₇(b_g): 71.20 cm^?1 = 2×35.6 cm^?1, 71.20 cm^?1 = 120.20 cm^?1 ?49.0 cm^?1: ω₂(a_g): 82.40 cm^?1 = 57.50 cm^?1 +24.9 cm^?1, 82.40 cm^?1 = 138.4 cm^?1 ?56 cm^?1. The efficiency of the down- and up-processes is discussed in terms of the two-phonon density of states. The bandwidths at 2 K follows very closely the variation of the two-phonon sum density of states, whereas the relative importance of the up-processes follows well the two-phonon difference density of states. The anharmonic frequency shifts are corrected for the thermal expansion of the crystal using the Grüneisen single-phonon parameters and the thermal expansion coefficients given in the literature. This permits an estimation of the variation of the anharmonic shifts in the temperature range studied.