A lattice gas model for the Zener relaxation

Abstract

The Zener relaxation is an anelastic relaxation process in disordered crystals due to stress-induced changes of atomic order. We present a model calculation of this process for a simple cubic lattice gas which is non-interacting except for the exclusion of multiple occupancies. The relaxation results from the stress-induced formation and dissolution of bonds between (paired) lattice gas atoms on nearest-neighbour sites. Relaxation spectra are obtained for the compressibility s 11 +2s 12 and the shear compliance s 11 −s 12 . The spectra are proportional to c 2 (1−c) 2 , where c is the occupation probability of a given site. The frequency dependence of the spectra is determined by the jump rate of the lattice gas atoms. Compared with a spectrum for a single relaxation time, the spectrum of s 11 − s 12 is moderately broadened, whereas the spectrum of s 11 + 2s 12 shows a sizable broadening. The present results are applicable to both interstitial and substitutional alloys.

Diffusion of Hydrogen and Deuterium in Titanium Hydride and Deuteride

“…We determine the jump rates of t 1 e H with the help of a recent theoretical model for the Zener relaxation [7]. An extrapolation of the jump rates towards higher temperatures agrees well with previous quasielastic neutron scattering (QNS) [2] and nuclear magnetic resonance (NMR) data, measured between 400 and 1200 K.…”

“…With the help of a recent model calculation for the Zener relaxation [7], we determined the jump rates of the H interstitials in 6-phase TiH, from our measured relaxation peaks. The temperature dependence of the jump rate follows an Arrhenius relation with an activation enthalpy of (0.49 f 0.04) eV.…”

“…The host-lattice metal atoms can be assumed to be immobile whereas the H atoms can diffuse on their interstitial sublattice. The anelastic Zener relaxation of such a diffusing lattice gas was considered in a recent model calculation [7]. The model assumes a lattice gas that is non-interacting except for the fact that a given lattice site can be occupied only once.…”

Interactions between solute atoms in Fe–Si–Al–C alloys as studied by mechanical spectroscopy

“…In binary Fe-Al and Fe-Si, it is usually understood as a reorientation of Al-Al or Si-Si pairs, which are normally not isolated but part of a directional short-range order (e.g., "bonds" in a lattice-gas model [27]). The almost equal relaxation strengths in Fig.…”

H-induced anelasticity as a probe: Application to nanoscale quasicrystals

“…1c. Moreover, different mechanisms were identified in this latter case [8,23], like a Zener mechanism (reorientation of H-H pairs [24]) for the central peak and a long-range diffusion mechanism (intercrystalline Gorsky effect [9,25]) for the broad high-temperature peak. The latter mechanism requires an elastically anisotropic structure and should, consequently, not exist in amorphous or icosahedral phases.…”