Physical dispersion resulting from anelasticity is investigated from the point of view of linear viscoelastic models and causality relations. It is concluded that inasmuch as Q in the earth's mantle is nearly independent of frequency, at least in the seismic frequency band, a dispersion relation in the form of C(ω) = C(ω_r)[1 + (1/πQ_m) In (ω/ω_r)] must be used for correcting the effect of physical dispersion arising from anelasticity. (Here C(ω) is the phase velocity of either body waves, surface waves, or free oscillations, ω is the angular frequency, ωr is the reference angular frequency, and Q_m is the path average Q for body waves or Q of a surface wave or a mode of angular frequency ω; for surface waves and free oscillations, C(ω_r) should be understood as the phase velocity at ω computed by using the elastic moduli at ω = ω_r.) The values of Q outside the seismic frequency band affect mainly the absolute value of the phase velocity but do not affect significantly the relative dispersion within the seismic frequency band. Even if the microscopic mechanism of attenuation is nonlinear, this dispersion relation can be used if departure from elasticity is relatively small, so that the signal can be approximated by a superposition of propagating harmonic waves. Since surface wave and free oscillation Q is 100–500 for fundamental modes, a correction of 0.5–1.5% must be made for joint interpretation of body wave and surface wave data. This correction is nearly 1 order of magnitude larger than the uncertainties associated with these data and are therefore very significant. When this correction is made, the discrepancy between the observed surface wave phase velocities and free oscillation periods and those predicted by the Jeffreys or Gutenberg model becomes much smaller than has previously been considered.

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Importance of physical dispersion in surface wave and free oscillation problems: Review

https://repository.brynmawr.edu/cgi/viewcontent.cgi?article=1123&context=physics_pubs

Spectral densities and nuclear spin relaxation in solids

Magnetic amorphous alloys obtained by rapid quenching of the melt are excellent soft magnetic materials with a wide range of technological applications. They also represent a significant challenge to the scientific understanding of magnetic materials, since most of the existing theories of solids assume lattice periodicity. For these reasons, the magnetic and other properties of amorphous alloys have been very actively studied over the last decade. In recent years increasing attention has been directed to the fundamental understanding of the structural, thermal and magnetic properties of the amorphous alloys. It is not only scientifically but also technologically important to achieve such an understanding, since the amorphous alloys are, in many respects, so different from conventional crystalline magnetic materials. The author attempts to summarise recent progress in research on magnetic amorphous alloys and critically assesses the present level of understanding of this new class of magnetic materials, focusing mostly on the transition-metal-metalloid glasses. He starts with a review of early developments and a discussion on the nature of glasses and glass formation and proceeds to an extensive discussion of their atomic structure, both from the experimental and theoretical points of view.

https://iopscience.iop.org/article/10.1088/0034-4885/47/12/002/pdf

Magnetic amorphous alloys: physics and technological applications

The activation energy of high temperature internal friction

It is shown that a broad distribution of correlation times produces an apparent‐phase‐transition effect in the NMR spin—spin relaxation time just before the onset of rigid‐lattice behavior. NMR relaxation‐time data for liquid water filling the pores of a charcoal adsorbent provide a sensitive test of the theory. The occurrence of the apparent phase transition for molecules adsorbed on the surfaces of solids provides a method of estimating the spread of activation energies for surface diffusion and thereby provides a new method for studying the heterogeneity of surfaces.

Apparent Phase—Transition Effect in the NMR Spin—Spin Relaxation Time Caused by a Distribution of Correlation Times

Such phenomena as dielectric, magnetic, and anelastic relaxation are often described in terms of a distribution of relaxation times. It is shown that a relaxation process which exhibits a Gaussian distribution in the logarithm of the relaxation times (a "lognormal" distribution) can be specified completely by three parameters. These are: the mean relaxation time (τm) the, width of the distribution (β), and the magnitude of the relaxation (δJ). The relationships of these parameters to experimentally measurable functions are usually complicated. These relationships were obtained in numerical form by machine computation. Finally, a simple formula is derived which expresses the parameter β in terms of the widths of the distribution of the activation energies and that of the attempt frequencies.

B. S. Berry

Papers

Lognormal distribution function for describing anelastic and other relaxation processes I. theory and numerical computations