Universal enthalpy-entropy compensation rule for the deformation of metallic glasses

Yun-Jiang Wang, Meng Zhang, Lin Liu, Shigenobu Ogata, and L. H. Dai

Phys. Rev. B 92, 174118 – Published 23 November 2015

Abstract

The thermodynamic compensation law describing an empirical linear relationship between activation enthalpy and activation entropy has seldom been validated for amorphous solids. Here molecular dynamics simulations reveal a well-defined enthalpy-entropy compensation rule in a metallic glass (MG) over a wide temperature and stress range, spanning the glass transition induced by temperature and/or stress. Experiments on other MGs reproduce this law, suggesting that it applies universally to amorphous solids, so we extend it from crystals to amorphous solids. In the glassy state, the compensation temperature is found to agree with the thermal glass transition temperature $T_{g}$ ; whereas in the supercooled liquid region, the compensation temperature matches $\sim 1.4 T_{g}$ , at which the diffusion kinetics start to feel the roughness of the free-energy surface.

Received 3 July 2014
Revised 14 October 2015
Corrected 1 December 2015

DOI:https://doi.org/10.1103/PhysRevB.92.174118

Corrections

1 December 2015

Erratum

Publisher's Note: Universal enthalpy-entropy compensation rule for the deformation of metallic glasses [Phys. Rev. B 92, 174118 (2015)]

Yun-Jiang Wang, Meng Zhang, Lin Liu, Shigenobu Ogata, and L. H. Dai

Phys. Rev. B 92, 219902 (2015)

Authors & Affiliations

Yun-Jiang Wang^1,*, Meng Zhang^1,2, Lin Liu², Shigenobu Ogata^3,4,†, and L. H. Dai^1,‡

¹State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
²School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
³Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
⁴Center for Elements Strategy Initiative for Structural Materials (ESISM), Kyoto University, Sakyo, Kyoto 606-8501, Japan

^*yjwang@imech.ac.cn
^†ogata@me.es.osaka-u.ac.jp
^‡lhdai@lnm.imech.ac.cn

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Vol. 92, Iss. 17 — 1 November 2015

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Images

Figure 1
Atomistic shear deformation of ${Cu}_{50} {Zr}_{50}$ . (a) Schematic sketch of the atomistic shear deformation. (b) MD snapshots indicating homogeneous shear deformation with strain rate $10^{8} s^{- 1}$ and temperature 600 K. Atoms are colored according to their local von Mises strain $η_{i}^{Mises}$ of atom $i$ [47], which is implemented in atomeye [48]. Typical stress-strain curves at (c) 550 and (d) 750 K, respectively.
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Figure 2
Temperature- and stress-driven transition of deformation mechanisms in MG. (a) Correlation between strain rate and flow stress. Inset shows the variation in the stress exponent $n$ . (b) Activation volume decreases abruptly at temperature well below $T_{g} (0)$ , denoting a temperature- and stress-induced glass transition and a shift in the deformation mechanism. (c) Logarithmic strain rate vs stress. Slope change indicates a decrease in activation volume, which implies a stress-induced glass transition. (d) Viscosity contour against both temperature and stress. Plots indicate the glassy state in a low-temperature and low-stress regime, whereas the glass transition can be driven by either temperature or stress. (e) Schematics of deformation regimes defined by $T_{g} (0)$ and the temperature-dependent critical stress $τ_{c} (T)$ . Regime I (glassy state): $T < T_{g}$ (0), $τ < τ_{c} (T)$ , where $τ_{c} (T)$ is determined by $\frac{T}{T_{g} (0)} + {[\frac{τ}{τ_{c} (0)}]}^{2} = 1$ . Regime II (supercooled liquid): $τ > τ_{c} (T)$ , but within $\frac{T}{T_{g} (0)} + {[\frac{τ}{τ_{c} (0)}]}^{2} = 1.4$ . Regime III (liquid): outside regime II.
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Figure 3
Enthalpy-entropy compensation rule in MG revealed by MD. (a), (b) Activation free energy as a function of stress at temperatures above and below $T_{g} (0)$ , respectively. Solid curves represent nonlinear fits. Shaded area in (a) denotes a stress-induced transition of the deformation mechanism. (c), (d) Established linear relationship between $Δ S$ and $Δ H$ in (c) regime I and (d) regime II.
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Figure 4
Experimental support of compensation rule via compression of Vit 1; the data are from Ref. [54]. (a) Strain-rate-modulated stress at different temperatures. (b) Activation free energy as a function of stress at different temperatures. (c) Linear fits of activation energy [above $T_{g} (0) = 624$ K] as a function of temperature. Data in the shaded area are excluded due to change of mechanism. Inset shows that the activation volume is in agreement with regime II. (d) Enthalpy-entropy compensation. The red line represents a best fit with $T_{MN}^{I} = T_{g} (0) = 624$ K; the blue line denotes a best fit with $T_{MN}^{II} = 1.4 T_{g} (0) = 874$ K. The theoretical predictions qualitatively agree with experimental data, while $T_{MN}^{II}$ yields a better agreement.
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Figure 5
Understanding of critical temperatures of MGs, which correlate with $T_{MN}$ . Arrhenius plot of the diffusion coefficient against temperature in the ${Cu}_{50} {Zr}_{50}$ . A critical temperature $T_{c}^{diff} \sim 950$ K $\sim 1.4 T_{g} (0)$ exists at which diffusion deviates from the Arrhenius relationship from the high-temperature limit. Atomic diffusion starts to feel the roughness of the free-energy surface. This critical temperature agrees with $T_{MN}^{II} = 970 \pm 40$ K for regime II. Inset shows the cooling history, which yields $T_{g} (0) = 675$ K, coinciding with $T_{MN}^{I} = 687 \pm 51$ K for regime I.
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