Wide-amplitude vibrations

Even for barriers as high as 3.5kcal/mol, when 0 — 200 cm"1, (2) — 0.2 rad, so that zero-point linear displacements of H atoms are 0.20-0.22 A. Thus, the torsion vibrations, unlike stretching modes, are really motions with wide amplitudes in the full sense of these words. The temperature dependence of can be found in the harmonic approximation using (2.82) experimentally, it can be extracted from the temperature dependence of the width of INS peaks assigned to torsion vibrations. As a typical example of this dependence, the results of Trevino et al. [1980] for deuterated nitromethane crystal are represented in Figure 7.8. 

There are certain manifestations of H-bonds which are either centrosymmetric or in which the transfer potential contains a broad minimum, or a pair of minima separated by a low barrier. In such cases, the proton position can be easily shifted by external influences and its vibration extends over a wide amplitude. Consequently, the infrared spectrum con-... 

Figure 10.6 A 2-D potential energy surface and the corresponding contour plot of the "T" shaped conformation of Ar-HCCH in the acetylene ground vibrational energy level. This X-Y coordinate plot shows the wide amplitude motion of the Ar atom around the acetylene unit. Taken with permission from Bemish et al. (1993).

Van der Waals complexes containing monomers with large rotational constants, such as HF, HCl, H2O and NH3, undergo very wide-amplitude bending motions even in low vibrational states. These states are best understood using quantum numbers derived from a free internal rotor picture, rather than those derived from the conventional near-rigid picture. The anisotropy of the potential splits and shifts the monomer free-rotor states, but the qualitative pattern of energy levels and allowed transitions remains. 

Random, low amplitude wide frequency vibration is often associated with vane pass frequency, resulting in vibrations similar to cavitation and turbulence, but it is usually found at lower frequencies. This can lead to misdiagnosis. Many pump impellers show metal reduction and pitting on the general area at the exit lips of the vanes. This has often been misdiagnosed as cavitation. 

It appears that the vibrotactile feedback is well perceived by the user thanks to the wide range of frequency and amplitude vibration provided by the innovative combination of vibrotactile actuators. The next important step is the user evaluation to check if metaphors are relevant and effectively help students to memorize electronics concepts easier than before. 

A further distinction arises because for many solids under a wide variety of state conditions the constituent particles execute small amplitude vibrations about well defined equilibrium positions (noteworthy exceptions are plastic crystals). If this situation pertains it is possible to express rj,(t) = Rj,+uj,(t) the instantaneous position of particle i in terms of its mean position and its time dependent displacement uj (t). If uj is in some sense small with respect to Rj one can develop F(Q,t) as a power series in g u. This is the so-called phonon expansion (10)... 

A practical procedure for tuning the frequency starts with acquisition of a spectrum of the non-linear response. With amplitude modulation applied, the ultrasonic vibration frequency is swept over a wide interval centred at the nominal resonance frequency of the piezoelectric transducer. From this spectrum, one finds the frequencies at which a non-linear response can... 

---