Microscopic description of flow defects and relaxation in metallic glasses

The anelastic relaxation behavior of amorphous $\mathrm{A}{\mathrm{l}}_{86.8}\mathrm{N}{\mathrm{i}}_{3.7}{\mathrm{Y}}_{9.5}$ was characterized in prolonged, quasistatic measurements, up to $1.1\times {10}^8\mathrm{s}$. The size-density distribution of potential shear transformation zones was determined from the data. We derive an expression for the distribution, based on a free-volume criterion for an atomic cluster being a potential shear transformation zone. The model is shown to be consistent with experiment.

Figure 1

Representative normalized anelastic strain vs time curves under fixed stress (cantilever experiment [17]) and stress-free (mandrel experiment after constraining for $4.4\times {10}^7\mathrm{s}$) for as-quenched samples. For the former, “×10” indicates that the values displayed are ten times the measured values. For the latter, data were obtained for two radii and corresponding elastic strain at mechanical equilibrium, ${\varepsilon }_{el}^0=0.184\%$ (+) and 0.237% (open circles). The relaxation-time spectra, $f\left(\tau \right)$ (filled and open circles, respectively, for the mandrel experiments), are computed from these curves [17, 21]. The integer peak index, $n$, was selected to reflect the fact that it is approximately equal to ${\Omega }_n/V_{\mathrm{Al}}$ (see Fig. 2).

Figure 2

Linear solid model: $N$ anelastic units act in series, where $n$-type sites are associated with Young's modulus of $E_n^{\prime }$ and viscosity ${\eta }_n^{\prime }$, both effective quantities that are inversely proportional to the volume fraction occupied by these sites.

Figure 3

Size-density distribution of STZs, $c_n$ as a function of $n$, calculated from the data (bars) and fitted with $c_n^{\mathrm{model}}$ from Eqs. (5) and (6) (curves) with fixed or variable $v^{*}$. The lines are guides to the eye.

Figure 4

Relaxation-time spectra for as-quenched and structurally relaxed samples following constraint for $2\times {10}^6\mathrm{s}$, indicating a decrease in the number of PSTZs upon structural relaxation.