Atomistic interpretation of the dynamic response of glasses
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Atomistic interpretation of the dynamic response of glasses JongDoo Ju, Department of Materials Science and Engineering, The University of Michigan, Ann Arbor, Michigan Michael Atzmon, Department of Nuclear Engineering and Radiological Sciences & Department of Materials Science and Engineering, The University of Michigan, Ann Arbor, Michigan Address all correspondence to Michael Atzmon at [email protected] (Received 3 December 2013; accepted 17 April 2014)
Abstract Using detailed information on the spectrum of shear transformation dynamics previously obtained from low-strain, quasi-static anelastic relaxation in a metallic glass, the corresponding response to a cyclic force is calculated, and prevailing analysis approaches are evaluated. It is shown that the time–temperature superposition principle does not resolve the distribution of activation energies for shear transformations. The distribution of shear transformation zone sizes explains the microscopic mechanisms of both slow (α) and fast (β) relaxations, and the fact that the former are irreversible. These results suggest the need to re-evaluate past interpretations of dynamic behavior of glasses.
Introduction The mechanical or dielectric response of a material to a cyclic force is a powerful probe of relaxation mechanisms over time constants spanning many orders of magnitude. For example, the loss modulus, i.e., the imaginary part of the dynamic modulus is measured as a function of temperature and angular frequency, ω. Identification of the microscopic processes underlying observed glass behavior has been a long-term challenge.[1] Based on the time–temperature superposition principle,[2–5] when frequency response curves obtained at different temperature can be shifted on a ln(ω) scale to yield a single master curve, a single activated process is typically concluded. The temperature dependence of the shift factor has been used to obtain an apparent activation energy. However, it has been observed consistently that the response curves are broader than a Cauchy function, the expected shape for a single time constant. Typically, a Kohlrausch– Williams–Watts (KWW) stretched exponent, exp[−(t/τ)β],[6–8] where β and τ are constants, or other functions are used as empirical descriptions of time-dependent relaxation.[4,9] This implicit a priori assumption about the shape of the relaxationtime spectrum strongly suggests a spread in activation energies. In many glasses, a tail is observed in the loss modulus or dielectric loss at fixed temperature and high frequencies, or at fixed frequency and low temperature. It has been attributed to (β) relaxation processes that differ qualitatively from those responsible for the main part of the peak, which originates from slower (α) relaxations.[10–13] We have recently obtained[14] relaxation-time spectra at room temperature, fRT(τ), directly from quasi-static anelastic relaxation measurements in amorphous Al86.8Ni3.7Y9.5 for time periods over 7 × 107 s. No a priori assumption was made
about the shape of the spectra.
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