Oscillation, rigorous calculations

In Equation 3.116, is rigorously defined as [(an - 022)I(S 2 > 1 is the sum of a constant term and two oscillating terms, accounted by ijr[ and y i is the strain rate amplitude. Equations 6 to 8 suggest that oscillatory shear stress data are related to oscillatory primary normal stress difference data (Ferry, 1980). Youn and Rao (2003) calculated values of (co) for starch dispersions is applicable to oscillatory shear fields. 

The input data required in calculating fractionation factors are the vibrational frequencies of all chemical species participating in an isotope exchange reaction. In many cases, however, frequencies have only been measured for molecules made with the abundant isotope (e g. 0) the frequencies of molecules containing the rare isotope (e.g. O) must be calculated. The simplest way to calculate the unknown frequencies is through the harmonic oscillator approximation (Eqn. 4). More rigorous and accurate calculations of frequencies require force-field models, which are available for many common gaseous molecules (e.g. Richet et al. 1977). 

If the complete details of the lattice modes are known, together with the way in which they evolve with temperature, the mean-square amplitudes can be calculated from them, and the temperature-dependence of the NQR frequencies predicted [10, 11], Such a rigorous approach need not be our concern here and it will suffice to note that only oscillations about the axes perpendicular to the field-gradient z-axis have any effect on either the coupling constant or the asymmetry parameter. 

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