Anomalous elastic response of amorphous alloys suggesting collective motions of many atoms

The dynamic Young’s modulus, E, of amorphous (a-) Zr₆₀Cu₃₀Al₁₀ (numbers indicate at.%) alloy was measured as a function of frequency, f, with a strain amplitude, _t, of 10^?6, E(10^?6,f), and also as a function of _t for f near 10² Hz, E(_t,10² Hz), by means of the vibrating reed methods. The elasticity study under the passing of electric current (PEC) was carried out too. E(10^?6,f) is lower than E₀ for f between 10 and 10⁴ Hz showing local minima near 5×10, 5×10² and 5×10³ Hz, which are indicative of the resonant collective motion of many atoms, where E₀ is the static Young’s modulus. E(_t,10² Hz) increases showing saturation with increasing _t. Qualitatively, the outlines of E(10^?6,f) and E(_t,10² Hz) observed for a-Zr₆₀Cu₃₀Al₁₀ are similar to those reported for various a-alloys. Quantitatively, a change in E(_t,10² Hz) for a-Zr₆₀Cu₃₀Al₁₀ is smallest among that reported for various a-alloys, presumably reflecting that the crystallization volume, (ΔV/V)_x, is smallest for a-Zr₆₀Cu₃₀Al₁₀. The effective charge number, Z^*, estimated from the change in E(10^?6,10² Hz) due to PEC is 3.0×10⁵, which is comparable with Z^* reported for various a-alloys. We surmise that the number of atoms in the collective motions excited near 10² Hz is similar among various a-alloys. The E(10^?6,f) data suggest that the spatial sizes of the density fluctuations may show a distribution.