The β relaxation process of La-based amorphous alloy: Effect of annealing and strain amplitude

Meng Shao-Yi; Hao Qi; Lyu Guo-Jian; Qiao Ji-Chao

doi:10.7498/aps.72.20222389

Abstract

The dynamic relaxation process of amorphous alloys is an important issue to understand the diffusion behavior, plastic deformation as well as glass transition phenomenon. In the current research, (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with a pronounced β relaxation process was selected as a model system to study the dynamic mechanical relaxation processes. Influence of driving frequency, physical aging and applied strain amplitude on the β relaxation of the La-based metallic glass was probed process using dynamic mechanical analysis. The experimental results demonstrated that the peak of the β relaxation process shifts to high temperature by increasing the driving frequency. Physical aging below the glass transition temperature induces a decrease of the intensity of the β relaxation process. The “defects” of amorphous alloy decreases during the physical aging process, which is ascribed to the glassy system shifts to more stable state induced by physical aging treatment. In parallel, the intensity of the β relaxation process of the amorphous alloy increases by increasing strain amplitude. The research sheds new light on further understanding the physical origin of β relaxation process of the amorphous alloy.

Keywords:

Authors and contacts

School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding author: Qiao Ji-Chao, qjczy@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51971178, 52271153), and the Outstanding Youth Found of Shaanxi Province, China (Grant No. 2021JC-12 ).

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References

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Cited By

图 1 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金X射线衍射图谱; (b) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金DSC曲线

Figure 1. (a) XRD pattern of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy; (b) DSC curve of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy.

DownLoad: Full-Size Img PowerPoint

图 2 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金归一化储能模量${E'}/{{E}}_{\text{u}}$和损耗模量${E''}/{{E}}_{\text{u}}$随温度的演化(升温速率: 3 K/min, 加载频率: 0.7 Hz); (b) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金归一化损耗模量${E''}/{{E}}_{\text{u}}$在不同加载频率随温度的演化 (升温速率为3 K/min). 插图是β弛豫峰温与加载频率的关系, 实线为Arrhenius方程拟合

Figure 2. (a) Temperature dependence of the normalized storage modulus ${E'}/{{E}}_{\text{u}}$ and loss modulus ${E''}/{{E}}_{\text{u}}$ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy (heating rate: 3 K/min , driving frequency: 0.7 Hz); (b) temperature dependence of the normalized loss modulus ${E''}/{{E}}_{\text{u}}$ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different frequency. 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非晶合金损耗模量${E''}/{{E}}_{\text{u}}$随加载频率演化; (b) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金等温和连续加热条件下β弛豫峰温与频率的关系, 实线为Arrhenius方程拟合

Figure 3. (a) Frequency dependence of the normalized loss modulus ${E''}/{{E}}_{\text{u}}$ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different temperature; (b) the frequency versus peak temperature of the β relaxation with different states (isochronal mode and frequency sweep mode), the solid line is the Arrhenius equation fit.

DownLoad: Full-Size Img PowerPoint

图 4 (a) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金等温原位退火过程储能模量${E'}/{{E}}_{\text{u}}$和内耗$ \tan\delta $随退火时间演化(退火温度为403 K, 加载频率为1 Hz, 实线为KWW拟合); (b) (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金在铸态和退火态(退火样品的退火温度为403 K, 退火时间为10 h)储能模量和损耗模量随温度演化过程(升温速率: 3 K/min, 加载频率: 1 Hz)

Figure 4. (a) Time dependence of the loss factor $ \tan\delta $ and normalized storage modulus ${E'}/{{E}}_{\text{u}}$ of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy, annealing temperature is 403 K, driving frequency is 1 Hz, the solid line is the best fitting by the KWW equation); (b) annealing temperature is 403 K, annealing time is 10 h, temperature dependence of the normalized storage modulus ${E'}/{{E}}_{\text{u}}$ and loss modulus ${E''}/{{E}}_{\text{u}}$ of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different states (as-cast and annealed state, heating rate: 3 K/min driving frequency: 1 Hz).

DownLoad: Full-Size Img PowerPoint

图 5 退火与β弛豫在微观结构角度的关系示意图

Figure 5. Schematic diagram of the relationship between annealing and β relaxation from the microstructural perspective.

DownLoad: Full-Size Img PowerPoint

图 6 (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金铸态和退火态Arrhenius方程拟合结果

Figure 6. The frequency versus peak temperature of the β relaxation process with different states (as-cast and annealed states), the solid line is the Arrhenius equation fit.

DownLoad: Full-Size Img PowerPoint

图 7 不同应变下(La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金归一化损耗模量${E''}/{{E}}_{\text{u}}$随温度演化 (升温速率为3 K/min)

Figure 7. Temperature dependence of the normalized loss modulus ${E''}/{{E}}_{\text{u}}$ for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy with different strain (heating rate: 3 K/min).

DownLoad: Full-Size Img PowerPoint

图 8 不同应变下(La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金的激活能线性拟合结果

Figure 8. Results of linear fitting of the activation energy of (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloys with different strain

DownLoad: Full-Size Img PowerPoint

图 9 (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅非晶合金激活能随应变演化示意图

Figure 9. Strain dependence of activation energy for (La_0.6Ce_0.4)₆₅Al₁₀Co₂₅ amorphous alloy.

DownLoad: Full-Size Img PowerPoint

[1]	Demetriou M D, Launey M E, Garrett G, et al. 2011 Nat. Mater. 10 123 Google Scholar
[2]	Hufnagel T C, Schuh C A, Falk M L 2016 Acta Mater. 109 375 Google Scholar
[3]	Inoue A 2000 Acta Mater. 48 279 Google Scholar
[4]	Johnson W, Samwer K 2005 Phys. Rev. Lett. 95 195501 Google Scholar
[5]	Ketov S V, Sun Y H, Nachum S, Lu Z, Checchi A, Beraldin A R, Bai H Y, Wang W H, Louzguine-Luzgin D V, Carpenter M A, Greer A L 2015 Nature 524 200 Google Scholar
[6]	Schuh C A, Hufnagel T C, Ramamurty U 2007 Acta Mater. 55 4067 Google Scholar
[7]	Wang W H 2012 Prog. Mater. Sci. 57 487 Google Scholar
[8]	Wang W H 2012 Nat. Mater. 11 275 Google Scholar
[9]	Wang W H 2019 Prog. Mater. Sci. 106 100561 Google Scholar
[10]	汪卫华 2013 物理学进展 33 177 Wang W H 2013 Prog. Phys. 33 177
[11]	乔吉超, 张浪渟, 童钰, 吕国建, 郝奇, 陶凯 2022 力学进展 52 117 Qiao J C, Zhang L T, Tong Y, Lyu G J, Hao Q, Tao K 2022 Adv. Mech. 52 117
[12]	Huang B, Zhu Z G, Ge T P, Bai H Y, Sun B A, Yang Y, Liu C T, Wang W H 2016 Acta Mater. 110 73 Google Scholar
[13]	Ichitsubo T, Matsubara E, Yamamoto T, Chen H, Nishiyama N, Saida J, Anazawa K 2005 Phys. Rev. Lett. 95 245501 Google Scholar
[14]	Liu Y H, Wang D, Nakajima K, Zhang W, Hirata A, Nishi T, Inoue A, Chen M W 2011 Phys. Rev. Lett. 106 125504 Google Scholar
[15]	Wang W H, Yang Y, Nieh T G, Liu C T 2015 Intermetallics 67 81 Google Scholar
[16]	Ye J C, Lu J, Liu C T, Wang Q, Yang Y 2010 Nat. Mater. 9 619 Google Scholar
[17]	王峥, 汪卫华 2017 物理学报 66 176105 Google Scholar Wang Z, Wang W H 2017 Acta. Phys. Sin. 66 176105 Google Scholar
[18]	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
[19]	Duan Y J, Zhang L T, Qiao J C, et al. 2022 Phys. Rev. Lett. 129 175501 Google Scholar
[20]	Zhang L T, Wang Y J, Pineda E, Yang Y, Qiao J C 2022 Int. J. Plast. 157 103402 Google Scholar
[21]	Wagner H, Bedorf D, Kuechemann S, Schwabe M, Zhang B, Arnold W, Samwer K 2011 Nat. Mater. 10 439 Google Scholar
[22]	Dmowski W, Iwashita T, Chuang C P, Almer J, Egami T 2010 Phys. Rev. Lett. 105 205502 Google Scholar
[23]	Jiao W, Wen P, Peng H L, Bai H Y, Sun B A, Wang W H 2013 Appl. Phys. Lett. 102 101903 Google Scholar
[24]	Wang Z, Sun B A, Bai H Y, Wang W H 2014 Nat. Commun. 5 5823 Google Scholar
[25]	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. China Phys. Mech. Astr. 44 396 Google Scholar
[26]	Liu Y H, Wang G, Wang R J, Zhao D Q, Pan M X, Wang W H 2007 Science 315 1385 Google Scholar
[27]	Qiao J, Wang Q, Pelletier J, Kato H, Casalini R, Crespo D, Pineda E, Yao Y, Yang Y 2019 Prog. Mater. Sci. 104 250 Google Scholar
[28]	Yu H B, Wang W H, Samwer K 2013 Mater. Today 16 183 Google Scholar
[29]	Wang J, Zhang X, Jiang L, Qiao J 2019 Prog. Polym. Sci. 98 101160 Google Scholar
[30]	Qiao J C, Wang Q, Crespo D, Yang Y, Pelletier J M 2017 Chin. Phys. B 26 016402 Google Scholar
[31]	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 Y F 2010 Sci. Bull. 55 115
[32]	Wang X D, Ruta B, Xiong L H, et al. 2015 Acta Mater. 99 290 Google Scholar
[33]	Li N, Xu X, Zheng Z, Liu L 2014 Acta Mater. 65 400 Google Scholar
[34]	Yu H B, Samwer K, Wu Y, Wang W H 2012 Phys. Rev. Lett. 109 095508 Google Scholar
[35]	Hao Q, Lyu G J, Pineda E, Pelletier J M, Wang Y J, Yang Y, Qiao J C 2022 Int. J. Plast. 154 103288 Google Scholar
[36]	Li R, Pang S, Ma C, Zhang T 2007 Acta Mater. 55 3719 Google Scholar
[37]	Menard K P 2015 Dynamic Mechanical Analysis (3rd Ed.) (Place: Published: Crc Press)
[38]	Zhao Z F, Wen P, Wang W H, Shek C H 2006 Appl. Phys. Lett. 89 071920 Google Scholar
[39]	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
[40]	Yu H B, Samwer K 2014 Phys. Rev. B 90 144201 Google Scholar
[41]	Goldstein M 2011 J. Non-Cryst. Solids 357 249 Google Scholar
[42]	Ke H B, Zeng J F, Liu C T, Yang Y 2014 Mater. Sci. Technol. 30 560 Google Scholar
[43]	Yang Y, Zeng J F, Volland A, Blandin J J, Gravier S, Liu C T 2012 Acta Mater. 60 5260
[44]	Perez J 1990 Solid State Ionics 39 69 Google Scholar
[45]	Cavaille J Y, Perez J, Johari G P 1989 Phys. Rev. B 39 2411
[46]	Ngai K L, Capaccioli S 2004 Phys. Rev. E 69 031501 Google Scholar
[47]	Lunkenheimer P, Wehn R, Schneider U, Loidl A 2005 Phys. Rev. Lett. 95 055702 Google Scholar
[48]	Zhao Y, Shang B, Zhang B, Tong X, Ke H, Bai H, Wang W H 2022 Sci. Adv. 8 eabn3623 Google Scholar
[49]	Qiao J, Pelletier J-M, Casalini R 2013 J. Phys. Chem. B 117 13658 Google Scholar
[50]	Wen P, Zhao Z F, Pan M X, Wang W H 2010 Phys. Status Solidi 207 2693 Google Scholar
[51]	Zhu F, Nguyen H, Song S, Aji D P, Hirata A, Wang H, Nakajima K, Chen M 2016 Nat. Commun. 7 1
[52]	Hiki Y, Tanahashi M, Takeuchi S 2008 J. Non-Cryst. Solids 354 1780 Google Scholar
[53]	Angell C A 1988 J. Non-Cryst. Solids 102 205 Google Scholar
[54]	郝奇, 乔吉超, Jean-Marc Pelletier 2020 力学学报 52 360 Google Scholar Hao Q, Qiao J C, Pelletier J M 2020 Acta Mech. Sin. 52 360 Google Scholar
[55]	Wang Z, Yu H B, Wen P, Bai H Y, Wang W H 2011 J. Phys. Condens. Mat. 23 142202 Google Scholar
[56]	Liu Y H, Fujita T, Aji D P B, Matsuura M, Chen M W 2014 Nat. Commun. 5 3238 Google Scholar
[57]	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
[58]	Aji D P B, Johari G P 2015 J. Chem. Phys. 142 214501 Google Scholar
[59]	Johari G P 1976 Ann. Ny. Acad. Sci. 279 117 Google Scholar
[60]	Johari G P 2002 J. Non-Cryst. Solids 307-310 317
[61]	Johari G P, Goldstein M 1970 J. Chem. Phys. 53 2372 Google Scholar
[62]	Johari G P, Goldstein M 1971 J. Chem. Phys. 55 4245 Google Scholar
[63]	Perez J 1994 J. Food Eng. 22 89 Google Scholar
[64]	Wang Z, Wang W H 2019 Natl. Sci. Rev. 6 304 Google Scholar
[65]	Qiao J, Pelletier J-M, Esnouf C, Liu Y, Kato H 2014 J. Alloy. Compd. 607 139 Google Scholar
[66]	Gauthier C, David L, Ladouce L, Quinson R, Perez J 1997 J. Appl. Polym. Sci. 65 2517 Google Scholar
[67]	Sun Y, Concustell A, Greer A L 2016 Nat. Rev. Mater. 1 16039 Google Scholar

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Vol. 72, Issue 7 - 2023-04-05

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