Effects of cooling rate on <i>β</i> relaxation process and stress relaxation of La-based amorphous alloys

Meng Shao-Yi; Hao Qi; Wang Bing; Duan Ya-Juan; Qiao Ji-Chao

doi:10.7498/aps.73.20231417

Abstract

The dynamic relaxation process and stress relaxation process are two important processes which can reflect the microstructures of materials, for they are closely related to the diffusions, the glass transition phenomena and the microstructural heterogeneities. It is of great significance to explore the relationship among them. In the current research, the β-relaxation characteristics and stress relaxation behaviors of bulk and ribbon samples obtained by different cooling rates are systematically investigated by taking the typical La-based amorphous alloys as model systems. The experimental results demonstrate that the cooling rate is an important parameter for controlling the energy state of the glass system, which further affects its physical and mechanical properties. Based on the dynamical mechanical spectra, the larger the cooling rate, the greater the low-temperature internal friction is and the smaller the beta relaxation activation energy according to Arrhenius calculations, and the greater the broadening of the beta relaxation behavior in the temperature spectra, suggesting that the higher cooling rate leads to greater atomic mobility and a high degree of heterogeneity in the microstructure. Thermodynamic analysis is conducted to study the slow process of thermal activation and the fast process driven by stress. At low temperature, the activation volume of the strip sample is larger than that of the bulk sample, and the activation volume values of the two samples are almost the same, as the cooling rate only affect the β relaxation stage, but exert little effect on the α relaxation, which is consistent with the conclusion that the stress relaxation behavior and β relaxation behavior are related to the structural non-uniformity of the amorphous alloy. The stress relaxation tests show that the characteristic time of deformation decreases at higher cooling rate, the normalized stress decay is larger, it is easier to deform under an applied force field, and the deformation unit is more likely to activate to accommodate structural deformation. The correlation between stress relaxation and β relaxation of amorphous alloy is further confirmed, and the proportion of liquid-like region is proportional to the relaxation mode spectrum, which also shows that β relaxation and stress relaxation are consistent. Finally, by calculating relaxation enthalpy $ \Delta {H}_{{\mathrm{r}}{\mathrm{e}}{\mathrm{l}}} $, the variation of microstructure heterogeneity with cooling rate is experimentally verified. The research sheds new light on further clarifying the relationship among β relaxation, deformation and microstructural heterogeneity of the amorphous alloy.

Keywords:

Authors and contacts

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China
2.
School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
3.
Chongqing Innovation Center, Northwestern Polytechnical University, Chongqing 401135, China

Corresponding author: Wang Bing, wangbing0614@nwpu.edu.cn ; Qiao Ji-Chao, qjczy@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51971178, 52271153, 52101201), the Outstanding Youth Foundation of Shaanxi Province, China (Grant No. 2021JC-12), the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX0369), the Practical Innovation Ability Cultivation Fund for Postgraduate Students of Northwestern Polytechnical University, China (Grant No. PF2023088), and the Science and Technology Innovation Team Science Fund of Shaanxi Province, China (Grant No. 2021TD-14).

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References

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Cited By

图 1 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金内耗随温度演化(升温速率为2 K/min, 加载频率为1 Hz); (b) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金损耗模量随温度演化, 实线为准点缺陷公式拟合β弛豫结果

Figure 1. (a) Temperature dependence of the internal friction for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy (heating rate: 2 K/min, driving frequency: 1 Hz); (b) temperature dependence of the loss modulus $ {E}'' $ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy. The solid line is the β relaxation result fitted by QPD theory.

DownLoad: Full-Size Img PowerPoint

图 2 (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金不同加载频率归一化损耗模量$ {E''}/{E}_{{\mathrm{u}}} $随温度演化　(a)块体样品; (b) 条带样品; 升温速率为2 K/min; 插图为β弛豫峰温与加载频率关系, 实线为Arrhenius方程拟合

Figure 2. Temperature dependence of the normalized loss modulus ${E''}/{E}_{{\mathrm{u}}} $ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different frequency: (a) Bulk; (b) ribbon. Inset shows the frequency versus peak temperature of the β relaxation, the solid line is the Arrhenius equation fit.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 不同温度下(La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金块体样品归一化损耗模量$ {E''}/{E}_{{\mathrm{u}}} $随加载频率演化^[51]; (b) 不同温度下(La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金条带样品归一化损耗模量$ {E''}/{E}_{{\mathrm{u}}} $随加载频率演化; (c) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金块体样品和条带样品等温扫频条件β弛豫峰温和频率的关系, 实线为Arrhenius方程拟合; (d) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金块体样品和条带样品的损耗模量在320 K参考温度下主曲线(实线为(1)式拟合结果)

Figure 3. (a) Frequency dependence of the normalized loss modulus ${E''}/{E}_{{\mathrm{u}}} $ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different temperature (bulk); (b) frequency dependence of the normalized loss modulus ${E''}/{E}_{{\mathrm{u}}} $ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different temperature (ribbon); (c) the frequency versus peak temperature of the β relaxation with different states (bulk and ribbon), the solid line is the Arrhenius equation fit; (d) main curve of loss modulus for amorphous alloy with different states (bulk sample and ribbon sample) at 320 K (solid line is fitting result of Eq. (1)).

DownLoad: Full-Size Img PowerPoint

图 4 (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金在310—425 K 的应力弛豫曲线(实线为KWW 方程拟合结果)　(a) 块体样品; (b) 条带样品; (c) 370 K下块体样品及条带样品应力弛豫曲线; (d) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金应力弛豫过程中特征弛豫时间$ {\tau }_{{\mathrm{c}}} $对数随温度演化

Figure 4. Stress relaxation curve of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy from 310 K to 425 K (solid line is the fitting results based on KWW equation): (a) Bulk; (b) ribbon; (c) stress relaxation curves of 370 K for bulk and ribbon; (d) temperature dependence of the logarithm of characteristic relaxation time $ {\tau }_{{\mathrm{c}}} $ in stress relaxation process for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy.

DownLoad: Full-Size Img PowerPoint

图 5 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金块体样品$\ln(-\dot{\sigma }) $与应力关系; (b) 快过程和慢过程的激活体积随温度演化

Figure 5. (a) Dependence of $ \ln(-\dot{\sigma }) $ on stress for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy bulk sample; (b) temperature dependence of the derived activation volume for the fast and slow events.

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图 6 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金不同温度下应力弛豫曲线初始应力和最终应力演化; (b) $ \theta $随温度演化; (c) $ {\mathrm{d}}\theta /{\mathrm{d}}T $随温度演化

Figure 6. (a) Initial stress and terminal stress evolution of stress relaxation curves for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy at different temperatures; (b) temperature dependence of the $ \theta $ for bulk and ribbon samples; (c) temperature dependence of the $ {\mathrm{d}}\theta /{\mathrm{d}}T $ for bulk and ribbon samples.

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图 7 块体样品和条带样品(La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金DSC曲线

Figure 7. DSC curves of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy for bulk and ribbon samples.

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map

[1]	Angell C A 1996 Curr. Opin. Solid State Mater. Sci. 1 578 Google Scholar
[2]	Greer A L 1995 Science 267 1947 Google Scholar
[3]	Chang C, Zhang H P, Zhao R, Li F C, Luo P, Li M Z, Bai H Y 2022 Nat. Mater. 21 1240 Google Scholar
[4]	Qiao J C, Wang Q, Pelletier J M, Kato H, Casalini R, Crespo D, Pineda E, Yao Y, Yang Y 2019 Prog. Mater. Sci. 104 250
[5]	Wang Q, Liu J J, Ye Y F, Liu T T, Wang S, Liu C T, Lu J, Yang Y 2017 Mater. Today 20 293 Google Scholar
[6]	Wang Q, Shang Y H, Yang Y 2023 Mater. Futures 2 017501 Google Scholar
[7]	Wang W H 2019 Prog. Mater. Sci. 106 100561 Google Scholar
[8]	乔吉超, 张浪渟, 童钰, 吕国建, 郝奇, 陶凯 2022 力学进展 52 117 Google Scholar Qiao J C, Zhang L T, Tong Y, Lyu G J, Hao Q, Tao K 2022 Adv. Mech. 52 117 Google Scholar
[9]	Wang X D, Ruta B, Xiong L H, Zhang D W, Chushkin Y, Sheng H W, Lou H B, Cao Q P, Jiang J Z 2015 Acta Mater. 99 290 Google Scholar
[10]	胡丽娜, 张春芝, 岳远征, 边秀房 2010 科学通报 55 115 Hu L N, Zhang C Z, Yue Y Z, Bian X F 2010 Sci. Bull. 55 115
[11]	Capaccioli S, Paluch M, Prevosto D, Wang L M, Ngai K L 2012 J. Phys. Chem. Lett. 3 735 Google Scholar
[12]	Ngai K L, Wang Z, Gao X Q, Yu H B, Wang W H 2013 J. Chem. Phys. 139 014502 Google Scholar
[13]	Wang W H 2011 J. Appl. Phys. 110 053521 Google Scholar
[14]	Yu H B, Wang W H, Bai H Y, Wu Y, Chen M V 2010 Phys. Rev. B 81 220201 Google Scholar
[15]	Yu H B, Wang W H, Bai H Y, Samwer K 2014 Nat. Sci. Rev. 1 429 Google Scholar
[16]	Li N, Xu X N, Zheng Z Z, Liu L 2014 Acta Mater. 65 400 Google Scholar
[17]	Yu H B, Samwer K, Wu Y, Wang W H 2012 Phys. Rev. Lett. 109 095508 Google Scholar
[18]	Yu H B, Wang W H, Samwer K 2013 Mater. Today 16 183 Google Scholar
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[20]	Dyre J C 2006 Rev. Mod. Phys. 78 953 Google Scholar
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[22]	Goldstein M 2011 J. Non-Cryst. Solids 357 249 Google Scholar
[23]	Hu L, Yue Y 2009 J. Phys. Chem. C 113 15001 Google Scholar
[24]	Wang W H, Dong C, Shek C H 2004 Mater. Sci. Eng. , R 44 45 Google Scholar
[25]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[26]	Zhao L Z, Wang W H, Bai H Y 2014 J. Non-Cryst. Solids 405 207 Google Scholar
[27]	Ma Z J, Guo Y C, Li Y, Lugee T, Gao P H, Yang Z, Zeng X R 2015 J. Alloys Compd. 648 18 Google Scholar
[28]	Wang B, Shang B S, Gao X Q, Wang W H, Bai H Y, Pan M X, Guan P F 2016 J. Phys. Chem. Lett. 7 4945 Google Scholar
[29]	Zhang L T, Duan Y J, Wang Y J, Yang Y, Qiao J C 2023 Sci. China-Technol. Sci. 66 173 Google Scholar
[30]	Jiao W, Sun B A, Wen P, Bai H Y, Kong Q P, Wang W H 2013 Appl. Phys. Lett. 103 101903 Google Scholar
[31]	Ke H B, Zhang P, Sun B A, Zhang P G, Liu T W, Chen P H, Wu M, Huang H G 2019 J. Alloys Compd. 788 391 Google Scholar
[32]	Milkus R, Zaccone A 2017 Phys. Rev. E 95 023001 Google Scholar
[33]	Qiao J C, Wang Y J, Pelletier J M, Keer L M, Fine M E, Yao Y 2015 Acta Mater. 98 43 Google Scholar
[34]	Qiao J C, Wang Y J, Zhao L Z, Dai L H, Crespo D, Pelletier J M, Keer L M, Yao Y 2016 Phys. Rev. B 94 104203 Google Scholar
[35]	Liang S Y, Zhang L T, Wang B, Wang Y J, Pineda E, Qiao J C 2024 Intermetallics 164 108115 Google Scholar
[36]	Luo P, Li M X, Jiang H Y, Wen P, Bai H Y, Wang W H 2017 J. Appl. Phys. 121 135104 Google Scholar
[37]	Luo P, Wen P, Bai H Y, Ruta B, Wang W H 2017 Phys. Rev. Lett. 118 225901 Google Scholar
[38]	Jiao W, Wen P, Peng H L, Bai H Y, Sun B A, Wang W H 2013 Appl. Phys. Lett. 102 101903 Google Scholar
[39]	Wang Z, Sun B A, Bai H Y, Wang W H 2014 Nat. Commun. 5 5823 Google Scholar
[40]	汪卫华 2014 中国科学: 物理学力学天文学 44 396 Google Scholar Wang W H, 2014 Sci. Sin. Phys. Mech. Astr. 44 396 Google Scholar
[41]	Li R, Pang S, Ma C L, Zhang T 2007 Acta Mater. 55 3719 Google Scholar
[42]	Lin X H, Johnson W L 1995 J. Appl. Phys. 78 6514 Google Scholar
[43]	Perez J 1990 Solid State Ionics 39 69 Google Scholar
[44]	Perez J, Etienne S, Tatibouät J 1990 Phys. Status Solidi A 121 129 Google Scholar
[45]	Qiao J C, Pelletier J M 2014 J. Mater. Sci. Technol. 30 523 Google Scholar
[46]	Wang Q, Pelletier J M, Blandin J J, Suery M 2005 J. Non-Cryst. Solids 351 2224 Google Scholar
[47]	Perez J 2018 Physics and Mechanics of Amorphous Polymers (London: Routledge) pp117–119
[48]	Rinaldi R, Gaertner R, Chazeau L, Gauthier C 2011 Int. J. Non-Linear Mech. 46 496 Google Scholar
[49]	Evenson Z, Naleway S E, Wei S, Gross O, Kruzic J J, Gallino I, Possart W, Stommel M, Busch R 2014 Phys. Rev. B 89 174204 Google Scholar
[50]	Wang B, Gao X Q, Qiao J C 2024 Rare Met. Mater. Eng. 53 70 Google Scholar
[51]	孟绍怡, 郝奇, 吕国建, 乔吉超 2023 72 076101 Google Scholar Meng S Y, Hao Q, Lyu G J, Qiao J C 2023 Acta Phys. Sin. 72 076101 Google Scholar
[52]	Kawamura Y, Shibata T, Inoue A, Masumoto T 1999 Mater. Trans., JIM 40 335 Google Scholar
[53]	Rösner P, Samwer K, Lunkenheimer P 2004 Europhys. Lett. 68 226 Google Scholar
[54]	Zhang P, Maldonis J J, Liu Z, Schroers J, Voyles P M 2018 Nat. Commun. 9 1129 Google Scholar
[55]	Polk D E, Turnbull D 1972 Acta Metall. 20 493 Google Scholar
[56]	Spaepen F 1977 Acta Metall. 25 407 Google Scholar
[57]	Heggen M, Spaepen F, Feuerbacher M 2004 J. Appl. Phys. 97 033506
[58]	Fan Y, Iwashita T, Egami T 2014 Nat. Commun. 5 5083 Google Scholar
[59]	Fan Y, Iwashita T, Egami T 2015 Phys. Rev. Lett. 115 045501 Google Scholar
[60]	Duan Y J, Zhang L T, Qiao J C, Wang Y J, Yang Y, Wada T, Kato H, Pelletier J M, Pineda E, Crespo D 2022 Phys. Rev. Lett. 129 175501 Google Scholar
[61]	Mayr S G 2006 Phys. Rev. Lett. 97 195501 Google Scholar
[62]	Wagner H, Bedorf D, Küchemann S, Schwabe M, Zhang B, Arnold W, Samwer K 2011 Nat. Mater. 10 439 Google Scholar
[63]	Chen H S 1980 Rep. Prog. Phys. 43 353 Google Scholar
[64]	Zhang L T, Wang Y J, Yang Y, Qiao J C 2023 Sci. China Phys. Mech. 66 286111 Google Scholar
[65]	Afonin G V, Mitrofanov Y P, Kobelev N P, da Silva Pinto M W, Wilde G, Khonik V A 2019 Scr. Mater. 166 6 Google Scholar

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Vol. 73, Issue 3 - 2024-02-05

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Effects of cooling rate on β relaxation process and stress relaxation of La-based amorphous alloys

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Corresponding author: Wang Bing, wangbing0614@nwpu.edu.cn ; Qiao Ji-Chao, qjczy@nwpu.edu.cn

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Effects of cooling rate on β relaxation process and stress relaxation of La-based amorphous alloys

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Corresponding author: Wang Bing, wangbing0614@nwpu.edu.cn ; Qiao Ji-Chao, qjczy@nwpu.edu.cn

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