Modulated strain

The films are epitaxial in the sense that the lattice constant is intermediate between those of copper and nickel. As indicated above, that modulated strain is probably responsible for the increased hardness. Other authors (5) have tried to explain similar effects by stating that the layers were specifically oriented. Our example (6) demonstrates that these considerations must be reexamined since it was possible to achieve the effect in a crystalline multilayer deposited on an amorphous nickel-phosphorus underlayer. It appears that layer thickness is the important parameter here. 

A strain-modulated DMA parallels the temperature-modulated DSC discussed in Sect. 4.4. Figure 4.161 shows a comparison to the results in Figs. 4.90, written for a common phase lag 0. Note that the measured heat-flow rate HF(t) lags hehind the modulated temperature, while the measured shear stress advances ahead of the modulated strain. Besides modulation of strain, it is also easily possible to modulate the stress, and even temperature-modulation is possible and of interest for comparison of DMA to TMDSC, as was established recently [44]. 

Visualizing the detailed dynamics of polymers subjected to a modulated strain from plots such as the one shown in Figures 21.8 to 21.13 can be quite difficult. The fact that the bands in the in-phase and quadrature spectra have such different shapes indicates that the time dependence of the dichroism for each band in the spectrum is quite different, since the rate of reorientation of each functional group in the molecule when subjected to the effect of a modulated strain may well be determined by their local environment. The fact that these rates vary can be used to differentiate between highly overlapped bands, as can be seen in the N—H stretching region of the in-phase and quadrature spectra of nylon-11 shown in Figure 21.6. 

Modulation Spectroscopy can be very usefiil in evaluating strains induced by growth (lattice-mismatched systems) or processing procedures, such as reactive-ion etching or oxide formation. The size and magnitude of the strain can be evaluated from the shifrs and splitdngs of various spectral lines, such as. ) or... 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

According to the orbital phase theory, the Gloss s diradical 62 is predicted to have a triplet ground state due to the same orbital-phase topology as the TM (2). In derivatives of 62, electronic and steric effects of various substituents as well as ring strains in the cyclic diradicals have successfully been applied to modulate the... 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

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