Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Short-range order in some polymer melts from X-ray diffraction

Wide-angle X-ray diffraction measurements were performed on polymer melts of isotactic and syndiotactic polypropylene (IPP and SPP), poly(ethylenepropylene) (PEP), polystyrene (PS), polyisobutylene (PIB), and polyethylene (PE), to study the dependence of the short-range structure of polymer liquids on chain architecture. Total structure functions, which comprise intra- and intermolecular contributions, were derived from the scattering data. The trivial Fourier components of the intramolecular structure (C(SINGLE BOND)>C ≃ 1.54 Å and C(SINGLE BOND)C(SINGLE BOND)C ≃ 2.55 Å) were subtracted from the total structure functions. The remaining functions contain only those intramolecular contributions dependent on the chain's conformational degrees of freedom, plus the intramolecular contributions. The structural differences between the polymers in momentum space are discerned only when the trivial components are subtracted. This subtraction also reduces the effects of truncation errors on Fourier transformation to real space. The short-range structure of PIB appears very different compared to all the others, which correlates with anomalies in a number of physical properties for this polymer. © 1996 John Wiley & Sons, Inc.     

A two-sided Arnoldi algorithm with stopping criterion and MIMO selection procedure

In this paper we introduce a two-sided Arnoldi method for the reduction of high order linear systems and we propose useful extensions, first of all a stopping criterion to find a suitable order for the reduced model and secondly, a selection procedure to significantly improve the performance in the multi-input multi-output (MIMO) case. One application is in micro-electro-mechanical systems (MEMS). We consider a thermo-electric micro thruster model, and a comparison between the commonly used Arnoldi algorithm and the two-sided Arnoldi is performed.