Shear transformation zone analysis of anelastic relaxation of a metallic glass reveals distinct properties of α and β relaxations

Metallic glasses with pronounced high-frequency β relaxation in their dynamic-mechanical response have been observed to exhibit large plasticity. Due to their disordered atomic structure, it is challenging to identify the microscopic mechanisms of their relaxation behavior. Quasistatic anelastic relaxation measurements have been performed over 10 orders of magnitude of time on $\mathrm{L}{\mathrm{a}}_{55}\mathrm{N}{\mathrm{i}}_{20}\mathrm{A}{\mathrm{l}}_{25}$ metallic glass, which exhibits a strong β relaxation. The corresponding time-constant spectra were computed from the data—they contain a series of peaks corresponding to an atomically quantized hierarchy of shear transformation zones (STZs), where both the α and β relaxations are consistent with the STZ model. Two different regimes of activation-volume increment between the peaks are observed, suggesting the involvement of different elements in STZs corresponding to α vs β relaxations. Room-temperature structural relaxation significantly affects the former but not the latter.

Figure 1

Schematic illustration of (a) nanoindenter cantilever bending and (b) bend relaxation (“mandrel”). For the former, a fixed load P is applied on the sample for 200 s. The vertical displacement $h$ is monitored as a function of time. For the latter, the sample is constrained around a mandrel with a radius R for $2.0\times {10}^6\mathrm{s}$ and then relaxed stress-free for up to $3.2\times {10}^7\mathrm{s}$ while monitoring the evolution of radius of curvature $r$($t$).

Figure 2

Anelastic bending strain at the surface normalized by the equilibrium elastic strain vs measurement time for $\mathrm{L}{\mathrm{a}}_{55}\mathrm{N}{\mathrm{i}}_{20}\mathrm{A}{\mathrm{l}}_{25}$ ribbons with different RT aging times. (a) Nanoindenter cantilever bending. Each curve corresponds to an average of all samples with the same aging condition, and each point is an average of every 500 experimental data points. (b) Mandrel measurements. Data for all samples are shown, and the dashed lines have the same slope.

Figure 3

Normalized anelastic strain from mandrel measurements at four measurement times $t_i$ as a function of prior RT aging time $t_a$.

Figure 4

Relaxation-time spectra of $\mathrm{L}{\mathrm{a}}_{55}\mathrm{N}{\mathrm{i}}_{20}\mathrm{A}{\mathrm{l}}_{25}$ with different RT aging times. Distinct peaks are observed and labeled $m=1,...,8$. (a) Nanoindenter cantilever bending. Each curve corresponds to an average of all samples at the same aging condition. (b) Mandrel measurements. Two representative curves are shown for each RT aging time. The spectra are shifted upwards for clarity. $m\le 5$ peaks correspond to the β relaxation and $m\ge 6$ to the α relaxation (see discussion).

Figure 5

(a) Relaxation time constant (${\tau }_m$) of each STZ type ($m$) for different RT aging times. (b) Relaxation time constants as a function of RT aging time of different STZ types. Dashed lines are power-law fits.

Figure 6

STZ volume (${\mathrm{\Omega }}_m$) as a function STZ type ($m$) for samples aged $2.9\times {10}^7\mathrm{s}$. The error bars, < 0.7%, are smaller than the symbols. The slopes correspond to the volume increment between two adjacent ${\mathrm{\Omega }}_m$ values. The random error in these slopes is 2%–3%.

Figure 7

Calculated evolution of shear modulus (μ) during RT structural relaxation. The abscissa is a sum of RT aging time and half of measurement time, a rough estimate necessary because samples undergo structural relaxation during the measurement, and both the aging time and measurement time are of similar orders of magnitude.

Figure 8

Volume fraction occupied by $m$-type potential STZs, Eq. (3), as a function of activation free energy $\mathrm{\Delta }{F}_m$, Eq. (1), divided by kT for different RT aging times. Each symbol corresponds to one aging time value. Arrows show the direction of evolution with RT aging for each $m$. $m=6-8$ and beyond (not active at RT within the time range used) correspond to the α relaxation, and $m\le 5$ correspond to the β relaxation. The last two data points for $m=8$ STZs represent an underestimation due to lack of mechanical equilibration at the end of the constraining period for samples with large aging times and associated large ${\tau }_8$ values (see discussion).