Anelasticity defects

The resulting strain is also periodic with the same angular frequency but generally lags behind the stress because time is required for the growth (or decay) of the anelastic strain contributed by the point-defect re-population during each cycle. The strain may therefore be written... 

Measurements of <5 yield direct information about the magnitude of the energy dissipation and the phase angle. 0 measures the fractional energy loss per cycle due to the anelasticity and is often termed the internal friction. According to the discussion above, 8 will be a function of the frequency, to should approach zero at both low and high frequencies and will have a maximum at some intermediate frequency. The maximum occurs at a frequency that is the reciprocal of the relaxation time for the re-population of the point defects. 

The preceding analysis provides a powerful method for determining the diffusivities of species that produce an anelastic relaxation, such as the split-dumbbell interstitial point defects. A torsional pendulum can be used to find the frequency, u>p, corresponding to the Debye peak. The relaxation time is then calculated using the relation r = 1/ojp, and the diffusivity is obtained from the known relationships among the relaxation time, the jump frequency, and the diffusivity. For the split-dumbbell interstitials, the relaxation time is related to the jump frequency by Eq. 8.63, and the expression for the diffusivity (i.e., D = ra2/12), is derived in Exercise 8.6. Therefore, D = a2/18r. This method has been used to determine the diffusivities of a wide variety of interstitial species, particularly at low temperatures, where the jump frequency is low but still measurable through use of a torsion pendulum. A particularly important example is the determination of the diffusivity of C in b.c.c. Fe, which is taken up in Exercise 8.22. 

Solution. Using a torsion pendulum, find the anelastic relaxation time, r, by measuring the frequency of the Debye peak, cup, and applying the relation cupr = 1. Having r, the relationship between r and the C atom jump frequency F is found by using the procedure to find this relationship for the split-dumbbell interstitial point defects in Exercise 8.5. Assume the stress cycle shown in Fig. 8.16 and consider the anelastic relaxation that occurs just after the stress is removed. A C atom in a type 1 site can jump into two possible nearest-neighbor type 2 sites or two possible type 3 sites. Therefore,... 

Nowick, A. S. and Heller, W. R. (1965) Dielectric and anelastic relaxation of crystals containing point defects. Adv. Phys. 14, 101-66. 

A mobile population of hydrogen has also been observed by anelastic spectroscopy measurements that were carried out by Palombo et al. Heating NaAlIij doped with 2 mol% TiCl3 to 436 K introduces a thermally activated relaxation process with a frequency of 1 kHz at 70 K. This denotes the formation of a point defect with a very high mobility ( 5 x lO jumps/s at 70 K). The relaxation involves the reorientation of H around Ti. 

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