$\beta$ relaxation and low-temperature aging in a Au-based bulk metallic glass: From elastic properties to atomic-scale structure

The slow $\beta$ relaxation is understood to be a universal feature of glassy dynamics. Its presence in bulk metallic glasses (BMGs) is evidence of a broad relaxation time spectrum that extends to deep within the glassy state. Despite the breadth of research devoted to this phenomenon, its microscopic origin is still not fully understood. The low-temperature aging behavior and atomic structural rearrangements of a ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ BMG are investigated in the regime of the slow $\beta$ relaxation by employing an ensemble of experimental techniques such as high-intensity synchrotron x-ray scattering, modulated differential scanning calorimetry (MDSC), dynamic mechanical analysis (DMA), impulse excitation, and dilatometry. Evidence of a distinct slow $\beta$-relaxation regime is seen in the form of (1) an excess wing of the DMA loss modulus beginning at $\sim$50 ${}^{\circ }$C, (2) a crossover effect of elastic modulus with isothermal aging at 50${}^{\circ }$C, and (3) a broad, nonreversing and largely irreversible sub-$T_g$ endotherm in the MDSC results. Atomic rearrangements occurring at the onset of the measured slow $\beta$-relaxation temperature regime were found to be confined mainly to the short-range order length scale while no significant atomic rearrangements occur on the length scale of the medium-range order. Furthermore, evidence is presented that suggests the crossover effect in Young's modulus is due to the evolution of chemical short-range order. These results support the emergent picture of a dynamically heterogeneous glassy structure, in which low-temperature relaxation occurs through atomic rearrangements confined mostly to the short-range order length scale.

Figure 1

Normalized loss modulus determined at different frequencies by DMA for ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ using a heating rate of 0.05 K/s. The inset shows the values of $E^{\prime }$ and $E^{\prime \prime }$ as a function of temperature for a test frequency of $\nu$ = 1 Hz.

Figure 2

Normalized Young's modulus $E/E_0$ as a function of annealing time for samples annealed at 37${}^{\circ }$C and (top, red circles) and 50${}^{\circ }$C (bottom, blue squares). For better clarity, the data corresponding to an annealing temperature of 50${}^{\circ }$C are also shown on a logarithmic time scale (inset, bottom).

Figure 3

DSC up scans (endotherms up) at a heating rate of 0.33 K/s. Each sample was subjected to different thermal treatments: (a) as-cast, (b) annealing at 50${}^{\circ }$C for $\sim$1 s, (c) annealing at 50${}^{\circ }$C for 24 h, and (d) aging at room temperature (RT) for $\sim$1 year. The curves are vertically translated for better comparison.

Figure 4

MDSC thermograms of ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ showing (a) the total heat flow for the first and second heatings, (b) the separated reversing and nonreversing components for the first heating, and (c) the separated reversing and nonreversing components for the second heating. The shaded area shows the enthalpy associated with the sub-$T_g$ endotherm. The black arrows indicate the change in slope at 60${}^{\circ }$C observed in the reversing signals. The curves have been vertically translated for better comparison.

Figure 5

Total structure factor $S\left(Q\right)$ of an as-cast sample of ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ at $T_0$ = 0${}^{\circ }$C. The first structure factor maximum is located at a scattering vector of $Q_1\left(T_0\right)=2.826$ Å${}^{-1}$. The inset shows the pseudo-Voigt function (solid line) used to determine the peak parameters.

Figure 6

Relative atomic volume changes ${[Q_1\left(T_0\right)/Q_1\left(T\right)]}^3=V/V_0$ during thermal cycling: first heating from 0${}^{\circ }$C to 145${}^{\circ }$C (open squares), subsequent cooling from 145${}^{\circ }$C to 0${}^{\circ }$C (blue circles), and second heating from 0${}^{\circ }$C to 250${}^{\circ }$C (red triangles). The inset shows the difference $\Delta$ (green circles) between first and second heating runs.

Figure 7

Reduced pair distribution function $G\left(r\right)$ of an as-cast sample of ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ calculated from the $S\left(Q\right)$ at $T_0$ = 0${}^{\circ }$C. The peak maxima are labeled as $R_i$, where $i=1–5$. The first $G\left(r\right)$ peak $R_1$ (magenta circles, left inset) was fitted with a Gaussian function (solid line, left inset). The second split speak ($R_{21}$ and $R_{22}$, right inset) was fitted with a sum of two Gaussians.

Figure 8

(a) DSC up scans (endotherms up) of as-cast samples of ${\mathrm{Au}}_{49}$${\mathrm{Cu}}_{26.9}$${\mathrm{Si}}_{16.3}$${\mathrm{Ag}}_{5.5}$${\mathrm{Pd}}_{2.3}$ employed at various heating rates $q_H$. The peak temperature of the sub-$T_g$ endotherm $T_p$ is indicated by the downward triangle. The onset of the caloric glass transition $T_g^{\mathrm{onset}}$ is marked by the upward solid triangle. (b) Arrhenius fit (dashed line) of the temperature dependence of the inverse heating rate (downward triangles) yielding an apparent activation energy of $E_{\beta }^{\prime }$ = 88.9 $\pm$ 6.0 kJ/g atom ($\sim$0.92 eV).

Figure 9

(a) Reduced height of the first structure factor maximum $S\left(Q_1\right)/S\left[Q_1\left(T_0\right)\right]$ and (b) reduced FWHM $w/w\left(T_0\right)$ during thermal cycling. The glass transition $T_g^{\text{x-ray}}$ is apparent at $\sim$129${}^{\circ }$C in both peak parameters. The inset in (b) shows a magnification of $w/w\left(T_0\right)$, where the release of excess free volume just prior to the glass transition is reflected in a sharpening of the FWHM. In both peak parameters, a difference of $\sim$1% between the first and second heating runs at $T_0$ can be ascertained.

Figure 10

Reduced first $G\left(r\right)$ peak position $\Delta R_1/R_1\left(T_0\right)$ during thermal cycling (bottom). All three sets of data share a similar thermal expansion coefficient of ${\alpha }_{\mathrm{glass}}^{R_1}=5.72\times {10}^{-6}$ ${\mathrm{K}}^{-1}$ up to $\sim$60${}^{\circ }$C. The dilatometric thermal expansion data (shaded circles, top) are given as comparison and the linear thermal expansion coefficient is determined as ${\alpha }_{\mathrm{glass}}^{\mathrm{dil}}=1.98\times {10}^{-5}$ ${\mathrm{K}}^{-1}$.

Figure 11

Relative changes of the $G\left(r\right)$ maxima during heating $\Delta R_i/R_i\left(T_0\right)$, where $i=1–5$. The macroscopic linear thermal expansion curve $\Delta L/L_0$ taken from dilatometry measurements is reproduced here (solid line). The glass transition $T_g$ is evident by the negative and positive changes in slope of $R_1$ and $R_{3–5}$, respectively.

Figure 12

Relative changes in the first $S\left(Q\right)$ and $G\left(r\right)$ maxima, $Q_1\left(t_0\right)/Q_1\left(t\right)-1$ (blue circles) and $\Delta R_1/R\left(t_0\right)$ (red squares), respectively, as a function of annealing time at 50${}^{\circ }$C. The data corresponding to the initial heating ramp from 0${}^{\circ }$C–50${}^{\circ }$C are not shown here.

Figure 13

Evolution of the positions of the different $G\left(r\right)$ peak maxima, $\Delta R_i\left(t\right)/R\left(t_0\right)$, where $i=1–5$, with annealing time at 50${}^{\circ }$C. Note the scaling difference of 10${}^{-3}$ and 10${}^{-4}$ in (a) and (b), respectively. For comparison, the data corresponding to $R_1$ are shown in both (a) and (b).