Sachs-Teller mass

The spectra of solid ethene at 4 K and 80 K consisted of weak and shifted peaks superimposed on a broad backgroimd [72], The spectrum was broadened through recoil from the low-mass ethene molecule ( 2.7.5) as observed also for dihydrogen. When ethene is bound in a complex or to a surface its effective Sachs-Teller mass ( 2.6.5.1) is increased the recoil spectrum is weaker and the peaks due to the vibrational modes are stronger and sharper. The vibrational peaks of gaseous and solid ethene and ethene adsorbed by carbon are listed in Table 7.8. 

The INS spectroscopy of water ice is particularly demanding of the current world-wide suite of neutron spectrometers. Excellent energy transfer resolution is required, to provide data capable of discriminating between competing dynamical models. However, low Q values are also needed, to reduce the impact of the Debye-Waller factor from this very light molecular species (H2O has a Sachs-Teller mass about 2 amu). 

This can be seen in Fig. 9.9 where the phonon-wings and the higher overtones are shown and the fundamental transition spectra of H2O and D2O ice-VIII are shown separately. The effect of an improved Debye-Waller factor can be seen in the spectrum of D2O. It has a heavier Sachs-Teller mass and the bands appear at lower frequency and so lower Q. 

The general trend that the wavelength of the phonon modes depends approximately on the reduced mass M of the oscillating system like A M " is reasonably fulfilled just as the Lyddane-Sachs-Teller relation, connecting LO and TO frequencies with the optical and static dielectric constants, taken from table 19.6. 

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