Fractional population of gas molecules (boxes) and contributions to the overtone γ-factor of Eq. (8) (lines) as a function of vibrational energy range (in units of cm−1) at 295 K.
Fractional population of gas molecules (dark grey sticks) and contributions to the overtone γ-factor of Eq. (8) (light grey sticks) as a function of v tot = ∑ i v i at 295 K.
Fractional population of gas molecules (dark grey sticks) and contributions to the overtone γ-factor of Eq. (8) (light grey sticks) as a function of v 5 at 295 K.
Temperature dependence of the γ-factor for three overtones of SF6 (solid line curves). From top to bottom: 2ν6 (black solid line), 2ν5 (blue solid line), 2ν1 (red solid line). For comparison, the factors of the 2ν2 and 2ν3 overtones of CO2 have also been plotted (dashed line curves). In the inset, the γ-factor is shown as a function of reduced temperature T* = k B T/(hcν i ).
Absolute-calibrated spectra S iso (in units of cm3 amagat) as a function of Raman frequency ν (in units of cm−1) for 13 values of gas density ranging from 2 to 27 amagat (in the upward direction). In the inset, the product M 0 · ρ [M 0 is the experimental zeroth-order moment (in units of cm6) of the signal generated from a gas sample of density ρ] is shown as a function of ρ (in units of amagat). The linear dependence is evidence that the recorded band comes from isolated molecules alone.
Isotropic spectrum I iso (in units of cm3) as a function of Raman frequency ν (in units of cm−1) for 13 values of gas density ranging from 2 to 27 amagat (in the upward direction; same colors as in Fig. 5 ). The small differences between the spectra (especially at the top) is an indication of weak but distinguishable pressure-induced effects modifying the shape of the overtone. In the insets the half-width Γ/2 at -maximum and the band-top shift δ (in units of cm−1) are shown as a function of density ρ (in units of amagat).
States of SF6 sharing, at 295 K, 95% of the total gas population. The states are sorted in the order of decreasing probability. States occupied to <1% share 15% of the total fractional population. The vector denotes the sixuplet (v 1 v 2 v 3 v 4 v 5 v 6).
Partition functions of the different normal vibration modes. n i stands for the oscillator dimension. The total vibrational partition function amounts to Z = 3.141 at T = 295 K. ν i are given in cm−1. The calculation of Z i ’s was done analytically.
Energy distribution of fractional SF6 populations and contributions to the hotband γ-factor of the overtone. For the purpose of this table, these contributions were computed numerically in order to monitor their convergence to the value given by Eq. (8) .
Fractional populations of SF6 molecules and their contributions to the Raman intensity of the overtone for different values of the initial state vibrational number v 5 at 295 K. All contributions due to other modes have already been accounted for in the calculation of the entry values.
Scattering cross-sections for the overtone by using incident light polarized ⊥ to the scattering plane.
Values for and in units of .
Input data needed in Eq. (11) . Polarizability derivatives are in units; vibrational frequencies and force constants are in cm−1.
Article metrics loading...
Full text loading...