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

Abstract

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(ag), ω2(ag), ω6(bg) and ω7(bg) 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(ag) and ω6(bg) have a bandwidth at 2 K of 0.045 cm−1. The other two phonons ω7(bg) and ω2(ag) 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(ag): 49.45 cm−1 = 2×24.72 cm−1, 49.45 cm−1 = 98.45 cm−1 −49.0 cm−1; ω6(bg): 57.50 cm−1 = 2×28.75 cm−1, 57.50 cm−1 = 108.50 cm−1 −51.0 cm−1; ω7(bg): 71.20 cm−1 = 2×35.6 cm−1, 71.20 cm−1 = 120.20 cm−1 −49.0 cm−1: ω2(ag): 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.