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• W2107614886 abstract "A unified theory of viscosity and viscoelasticity of the molecular-rearrangement type is given in which the two phenomena appear as special cases. The Becker theorem is reviewed; with the Becker distribution of relaxances, the distribution function of activation energies is a constant, viscoelastic creep is logarithmic and the specific damping 1/Q is frequency insensitive in wide ranges of time and frequency. The vibrating-string theories of dislocation damping in general are not feasible because the mean thermal kinetic energy of the basic mode is smaller by an order of magnitude than the Peierls—Nabarro dissipation for amplitudes equal to the Burgers vector of most materials. Low-amplitude damping is treated as a consequence of the perturbation of the activation energies of thermally activated jumps of dislocation segments by the applied stress; since the distribution function of the activation energies is probably close to the Becker distribution, the resulting damping is insensitive to frequency and amplitude and increases steeply with the temperature. The Amontons law of solid friction breaks down at very small amplitudes of displacement, such as those between the walls of small cracks in rocks. The simplest generalization of the Amontons law to include small amplitudes leads to an amplitude- and frequency-independent damping. The effect of pressure on the viscosity, if regarded as given approximately by an increase of the activation energy by the product of the pressure and the volume expansion accompanying a molecular rearrangement, seems relatively small: with an expansion of 10 cubic Ångströms and a pressure of 1 megabar (2200 km depth), the increase is about 6eV corresponding to about 0·6eV at room temperature; with 4 cubic Ångströms, about 0·24eV. The grain boundary viscosity, therefore, should be relatively low. On the other hand, the crystal grains should be very hard in the deep mantle because the shear modulus is close to that of diamond at the core boundary. These factors seem to account for the creep and damping properties of the middle and deep mantle. The high damping and low viscosity in the Gutenberg low-velocity layer seems to be due to a phase transition, possibly including some eutectic grain boundary melting. While there is no general physical relationship between damping and creep, the parallelism expressed by Anderson's empirical formula seems to express the drastic decrease of both Q and η in the presence of a phase transition." @default.
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• W2107614886 date "2010-01-26" @default.
• W2107614886 modified "2023-09-23" @default.
• W2107614886 title "Seismic Damping and Creep in the Mantle" @default.
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• W2107614886 doi "https://doi.org/10.1111/j.1365-246x.1967.tb06237.x" @default.
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