Order parameter phase shift

With increasing values of P the molar volume is in progressively better agreement with the experimental values. Upon heating a phase transition takes place from the a phase to an orientationally disordered fee phase at the transition temperature where we find a jump in the molar volume (Fig. 6), the molecular energy, and in the order parameter. The transition temperature of our previous classical Monte Carlo study [290,291] is T = 42.5( 0.3) K, with increasing P, T is shifted to smaller values, and in the quantum limit we obtain = 38( 0.5) K, which represents a reduction of about 11% with respect to the classical value. 

This phase shift depends on x0, vx0 and ax0 at the same time, i.e., on the parameters needed for spin density, velocity and acceleration mapping, respectively. In order to distinguish the three quantities of interest, more sophisticated gradient pulse sequences have been designed, resulting in phase shifts that essentially depend only on a single parameter or a selection of parameters. 

For many systems and flow fields, the position dependent term dominates the phase shift while the velocity dependent term is still significantly larger than the acceleration dependent term. As a direct consequence, terms with a higher order of t than the term including the parameter to be evaluated may often be neglected,... 

Fig. 10 Temperature dependence of the average 0-H bond length as measured via the isotropic chemical shift for all carbon atoms in squaric acid. The change in the O bond length appears to play the role of an order parameter in the phase transition [20]...

Schwartz singularities are avoided using the Harris method, but results can only be obtained at the discrete energies Ep (although the values of Ep can be altered by changing the values of the non-linear parameters in the trial function). Furthermore, the error in the phase shift is only of first order in the error in the trial wave function, and the results may therefore be less accurate than those of a well-behaved Kohn calculation. 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

Oscillations of were found in SFS multilayers for different combinations of materials [19-28]. Typically at small F layer thickness, d, phase difference

between phases of superconductor order parameters is zero (so-called zero state). With a increase exhibits first a rapid drop with a minimum for some df. After this point increases with df saturating at larger thickness. This overall TJ dj ) behavior is a signature of the 0 -phase shift in S/F hybrids [2]. At large d the critical temperature for = r exceeds for [Pg.538]

This section presents a phenomenological description of those aspects of solid-state NMR spectroscopy that are most useful for obtaining structural and dynamical information on phase transitions in minerals and the nature of disordered phases. The chemical shift and nuclear quadrupole interactions and their anisotropies receive particular emphasis, because they provide sensitive probes of the short-range structure, symmetry, and dynamics at the atomic position. Frequency shifts arising from these interactions can also serve as physical properties from which order parameters can be obtained for use in Landau-type treatments of the evolution toward a phase transition. 

For the best resolved peaks corresponding to a pseudo-symmetric pair of sites (those at -88.7 and -90.5 ppm, for Timzi and Timzo, respectively) the difference in chemical shift could be related to the order parameter (Q) for the transition. The difference in chemical shift (A5) between a site in the P phase (e g., 5ximzo for the Timzo site) and its equivalent in the 71 phase just above Tc (5ximz for Tlmz Abximzo = 5ximz - bximzo) can be expressed in terms of 0 by a power series expansion ... 

A similar analysis applies to the triclinic-monoclinic (/T -72/c) transition that occurs at 298 K across the compositional join CaAl2Si208-SrAl2Si208 near 85 mol % Sr, except that the order parameter varies with composition with a form similar to Equation 7 (Phillips et al. 1997). With increasing Sr-content, the Si MAS-NMR spectra (Fig. 17) clearly show a decrease in the number of peaks that corresponds to a change in the number of crystallographically distinct Si sites from four (/1) to two (72/c). The order-parameter could be related to the difference in chemical shift between the Tlo site of the 72/c phase (-85.4 ppm) and the peak for the Tlmz site of the 71 samples, which is well-resolved and moves from -89.5 to -86.7 ppm with increasing Sr-content. These results yielded a critical exponent P = 0.49+0.2, consistent with the second-order character of the transition. 

NMR studies it has been observed that the long molecular axis is nearly parallel to the para- x s of the phenyl moiety and hence the first few fragments of the chain attached to the indazole group are not along this axis. This requires that the alkoxy chain attached to the indazole group has at least six carbon atoms to promote liquid crystalline behaviour. The order parameters of 4 -cyanophenyl 4-heptylbenzoate have been obtained by using 2D-NMR spectroscopy.Linear relationships between C-chemical shifts and order parameters have been obtained. Phase behaviour of a mixture of this liquid crystal and its chain-perfluorinated analogue has also been studied. 

The observed chemical shift in the nematic phase depends on the isotropic shift, the ordering parameters, and the elements of o.14... 

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