Spin scattering

The resistivities of the magnetic borides DyB, H0B12, ErB, and TmB, have been carefully measured by Gabani et al. (1999) for good quality crystals with low room temperature resistivities (10-30 p 2 cm) compared to the early work. Near the antiferromagnetic transition temperatures Tn, the resistivities all show small increases in the form of humps and then rapid drops as the temperature is lowered. This behavior can be explained as an initial increase in the resistivity attributed to the appearance of superzone boundaries within the Brillouin zone, followed by a decrease due to a reduction in spin scattering (Taylor and Darby, 1972 Fournier and Gratz, 1993). 

Figure 2(a) shows the ESR signal measured for two temperatures and fits using an assymetric Dysonian line shape. The fit allows us to determine the Lande g factor and the line width (AH) gives us a measurement of the spin scattering time ts using (f//// A//)rs = h. 

Figure 2(b) compares the thermal evolution of the MgB2 ESR linewidth (this work and Refs. [17, 18]) with its dc resistivity extract from Ref. [19]. The linewidth is measuring the spin scattering rate and the resistivity gives the... 

The proceedings of a conference on metal-ammonia solutions have been published, featuring reviews of the physical properties of dilute and concentrated solutions, electrical, n.m.r., i.r., and Raman spectroscopic studies of diffusion, the solvated electron, kinetics, and solution structure."" Electron spin resonance in metallic Li-NHa systems has been investigated from 12 to 296 K. In the liquid solutions and in the cubic phase of Li(NH3)4 the conduction e.s.r. lineshapes are in agreement with theory. To a good approximation the solvated ions are the only spin scatterers in the liquid state. The paramagnetic susceptibility of liquid Li(NH3)4 indicates that the concentration of localized moments is low and they order antiferromagnetically below 20 K." ... 

Isotope Natural abundance (%) Nuclear spin Scattering length, bcoh (10 cm)... 

In most cases, samples are a mixture of isotopes j with different scattering length bj and it is assumed that they are randomly distributed over the sample. Such random distribution of different isotopes produces incoherent cross-section. In analogy with isotope incoherence, spin incoherence is also observed. For nuclei with spin I l, the interaction depends on the orientation between neutron and nuclear spins scattering lengths and b for parallel and untiparallel spin, respectively, are different and the orientations of spins are randomly distributed in the nuclei even if they are the same kinds of nuclei. Then, incoherent and coherent atomic cross-sections are given by... 

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

For femhons with half-mtegral spin s, the statistical weights are = s/(2s + 1) and = (.s + l)/(2.s + 1). The differential cross section for fennion-fennion scattering is then... 

Cakmak M, Teitge A, Zachman FI G and White J L 1993 On-line small-angle and wide-angle x-ray scattering studies on melt-spinning poly(vinylidene fluoride) tape using synchrotron radiation J. Polym. Sc/. 31 371- 81... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

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