Relaxation Decoupling in Metallic Glasses at Low Temperatures

Upon cooling, glass-forming liquids experience a dynamic decoupling in the fast $\beta$ and slow $\alpha$ process, which has greatly influenced glass physics. By exploring an extremely wide temporal and temperature range, we find a surprising gradual change of the relaxation profile from a single-step to a two-step decay upon cooling in various metallic glasses. This behavior implies a decoupling of the relaxation in two different processes in a glass state: a faster one likely related to the anomalous stress-dominated microscopic dynamics, and a slower one associated with subdiffusive motion at larger scales with a broader distribution of relaxation times.

Figure 1

(a) Stress relaxation profiles of ${\mathrm{Zr}}_{44}{\mathrm{Ti}}_{11}{\mathrm{Cu}}_{10}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{25}$ MG, from bottom to top and left to right, $T=629$, 619, 609, 599, 589, 579, 569, 559, 539, 519, 499, 469, and 439 K. (b) ${\mathrm{La}}_{55}{\mathrm{Ni}}_{20}{\mathrm{Al}}_{25}$ MG, $T=472$, 462, 452, 442, 432, 422, 412, 402, 382, 362, 342, and 322 K. (c) ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{40}{\mathrm{Al}}_{10}$ MG, $T=693$, 683, 673, 663, 653, 643, 623, 603, 583, 563, 533, 503, and 473 K. In the stress relaxation experiments, a tensile strain $ϵ=0.3\%$ is applied on the MG ribbons. Solid lines are theoretical fits to the data. The obtained fitting parameters are plotted in Fig. 2.

Figure 2

The fitted relaxation rate (a) and exponent (b) as a function of $T_g/T$. Filled symbols represent ${\mathrm{\Gamma }}_0$ and ${\gamma }_0$, half-filled symbols ${\mathrm{\Gamma }}_1$ and ${\gamma }_1$, and open symbols ${\mathrm{\Gamma }}_2$ and ${\gamma }_2$; red squares refer to ${\mathrm{Zr}}_{44}{\mathrm{Ti}}_{11}{\mathrm{Cu}}_{10}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{25}$, green circles ${\mathrm{La}}_{55}{\mathrm{Ni}}_{20}{\mathrm{Al}}_{25}$, and blue triangles ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{40}{\mathrm{Al}}_{10}$ MG. The inset in panel (a) plots ${\mathrm{\Gamma }}_1$ of the three samples against $(1000\mathrm{K})/\mathrm{T}$. Error bars are given by the fitting, where they are not shown they are within the symbol size. Solid lines in panel (a) and the inset are the best linear fit.

Figure 3

(a) Stress relaxation profiles of ${\mathrm{La}}_{55}{\mathrm{Ni}}_{20}{\mathrm{Al}}_{25}$ MG of different ages: as-cast and pre-annealed at $0.9T_g$ (422 K) for a series of planned times, $t_a$. $ϵ=0.3\%$ and $T=422\mathrm{K}$. The data for the as-cast sample are fitted with Eq. (1) and the others Eq. (2). The inset shows the relaxation rate versus $t_a$, where the data for the as-cast sample is also plotted in the logarithmic coordinates at $t_a=0.1\mathrm{h}$. (b) Stress relaxation profiles of ${\mathrm{Zr}}_{44}{\mathrm{Ti}}_{11}{\mathrm{Cu}}_{10}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{25}$ MG at 519 K with different strains, fitted with Eq. (2). The lower left and upper right insets plot the relaxation rate and exponent, and $\sigma (0)$ versus strain, respectively.

Figure 4

Schematic Arrhenius diagram concerning dynamical behaviors of MG and its high temperature precursors. Data for $\alpha$ and the $\beta$ relaxations are from dynamical mechanical measurements on ${\mathrm{La}}_{55}{\mathrm{Ni}}_{20}{\mathrm{Al}}_{25}$ MG (Fig. S3 [16]). The red line is the Vogel-Fulcher-Tammann (VFT) [3] fit to the $\alpha$-relaxation data and the blue line the Arrhenius fit to the $\beta$-relaxation data.