Thermal vibrational excitation

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

Fig. 2. Surface temperature dependence of the vibrational excitation of NO(v = 0 — 1) in collisions with a clean Ag(lll) surface. The observed thermal activation was attributed to hot electron-hole-pair recombination transferring energy to NO vibration. This work provided some of the first strong evidence that metal electrons can interact with an adsorbate molecule strongly enough to change its vibrational quantum numbers. (See Ref. 24.)...

Remember that it is not the direct energy resonance between the vibrational levels in the two modes that is important. For cluster bond excitation, it is a resonance between the energy of the unoccupied vibrational levels in the weak cluster bond relative to the occupied excited level and quanta of thermal vibrational energy in... 

Electrons of still lower energy have been called subvibrational (Mozumder and Magee, 1967). These electrons are hot (epithermal) and must still lose energy to become thermal with energy (3/2)kBT — 0.0375 eV at T = 300 K. Subvibrational electrons are characterized not by forbiddenness of intramolecular vibrational excitation, but by their low cross section. Three avenues of energy loss of subvibrational electrons have been considered (1) elastic collision, (2) excitation of rotation (free or hindered), and (3) excitation of inter-molecular vibration (including, in crystals, lattice vibrations). 

At room temperature the thermal population of vibrational excited states is low, although not zero. Therefore, the initial state is the ground state, and the scattered photon will have lower energy than the exciting photon. This Stokes shifted scatter is what is usually observed in Raman spectroscopy. Figure la depicts Raman Stokes scattering. 

SM = iAM2 a measure of the distortion of the acceptor vibration in the excited state. A is the dimensionless, fractional displacement in normal vibration M between the thermally equilibrated excited and ground states. It is related to AQeq by A AQe ( )l/2, where M is the reduced mass for the vibration. 

This compound also possesses a comparatively large ionisation potential (15.3 eV)163,164, and one of the largest known cross-sections for the capture of thermal electrons. The latter process has been studied in considerable detail by beam, swarm and microwave techniques104 165-170. The initial attachment gives rise to a vibrationally excited ion169,17°, viz. 

The relative population ratio FJFi was slightly higher than expected from a 300 K thermal distribution (e.g. 2.1 vs 1.8). Of particular note, in comparison to a simple Boltzmann distribution, there was a substantial absence of population in the F2(J < S.S) levels from that expected based on a thermal (300 K) distribution. Approximately 1% of the desorbed molecules were vibrationally excited. 

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