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Intrinsic correlation between elastic modulus and atomic bond stiffness in metallic glasses
Materials Letters 175 (2016) 227–230
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Intrinsic correlation between elastic modulus and atomic bond stiffness in metallic glasses W. Zhao a,b, J.L. Cheng a,b, S.D. Feng c, G. Li c, R.P. Liu c,n a
School of Materials Science and Engineering, Nanjing Institute of Technology, Nanjing 211167, China Jiangsu Key Laboratory of Advanced Structural Materials and Application Technology, Nanjing 211167, China c State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 October 2015 Received in revised form 8 February 2016 Accepted 6 March 2016 Available online 8 March 2016
ZrxCu100 x (x ¼15–70) metallic glass (MG) models were constructed by molecular dynamics simulations to explore the intrinsic correlation between elastic modulus and atomic bond stiffness in MGs. The elastic modulus and atomic mole fraction of MGs approximately behave parabolically, and their maxima location shifts to lower Zr mole fraction. This phenomenon is due to the variation of their atomic bond percentages, which suggests that elastic modulus reflects the inherent stiffness of atomic bonds. The “rule of mixture”, which uses atomic bonds as the components, is more applicable than that in which atoms are used as the components to explain the inheritance of elastic modulus. & 2016 Elsevier B.V. All rights reserved.
Keywords: Atomic bond Elastic properties Amorphous materials Molecular dynamics simulation
1. Introduction The disordered atomic structure of metallic glasses (MGs) gives rise to their unique mechanical and physical properties, such as strength and elasticity, and this structure is considered for a wide range of applications [1–5]. Thus, the underlying mechanisms for the mechanical properties of MGs are fundamentally interesting. The development of MGs with efficient structure-property relationship is challenged by the complexity and uncertainty of their structure. To predict MG properties, the previous studies [6,7] achieved remarkable results in estimating elastic modulus by conducting weighted average on the elastic modulus of pure metal, that is, M = ∑ fi Mi , where M represents Young's modulus (E) or shear modulus (G), fi is the atomic fraction of the ith component, and Mi is E or G of the ith component. However, this method can hardly explains certain phenomena, such as the non-monotonic increase in the elastic modulus of Zr–Cu system with the increasing Cu element. The Young's modulus of pure Zr is 68 GPa, and that of pure Cu is 130 GPa [6]. Several important factors are neglected, and thus the unknown important factors should be explored to understand and control these properties. The macroscopic properties of a material are determined by atomic interaction in most cases, including selection of MGs. By using the atomic n
Corresponding author. E-mail address: [email protected] (R.P. Liu).
http://dx.doi.org/10.1016/j.matlet.2016.03.037 0167-577X/& 2016 Elsevier B.V. All rights reserved.
bond as the component and by utilizing the weighted average method (rule of mixture), the present work studies the elastic modulus of Zr–Cu MGs by molecular dynamics simulation, and this new “rule of mixture” can clarify the unexplained problems.
2. Simulation methods ZrxCu100 x MG models with x values of 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, and 70 were prepared. The simulations are performed by using the embedded atom method (EAM) potential [8], which is supplied in LAMMPS [9]. The dimension of the model structures, which are used in the calculations, are 17.1 nm 25.6 nm 4.3 nm in the x, y, and z directions, respectively. The model is heated from 300 K to 2500 K at a constant rate of 10 K/ps. To make the system in a natural state, we relax the liquid system for 50 ps at 2500 K within the NPT ensemble (namely constant number, constant pressure, and constant temperature) under periodic boundary condition by conjugated gradient method [10]. Subsequently, we cool the system from 2500 K to 100 K in 100 K decrements at a constant quenching rate of 5 K/ ps and zero external pressure. The temperature was controlled by Nose–Hoover thermostat method. To annihilate the defects in the models, 5 GPa hydrostatic pressure was initially applied to the models. Then, the atomic bond proportions and elastic modulus were estimated by partial coordination number and stress–strain curve analyses, respectively.
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W. Zhao et al. / Materials Letters 175 (2016) 227–230
3. Results and discussion Atoms are regarded as the elementary units of MGs in previous studies (Fig. 1(a)), whereas atomic bonds are considered as the elementary units of MGs in the current study (Fig. 1(b)). To apply the “rule of mixture” by using the atomic bonds as the components, the percentages of the different bonds in the Zr–Cu system should be calculated. Atomic bond proportion is a totally new parameter that can be calculated through the average partial coordination number and atomic mole fraction [11]. The total number of atoms in the Zr–Cu system is N, and the number of Zr atoms is xN, where x is the mole fraction of Zr. The number of Zr– Zr bonds can be expressed as xNNA-A/2, where NA-A is the Zr–Zr partial coordination number. Similarly, the number of Cu–Cu bonds can be expressed as (1 x)NNB-B/2, where NB-B is the Cu–Cu partial coordination number. The number of Zr–Cu bonds can be expressed as (xNNA-B þ(1 x)NNB-A)/2, where NA-B is the Zr–Cu partial coordination number, and NB-A is the Cu–Zr partial coordination number. Thus, the atomic bond proportion can be expressed as:
PA − A =
xNA − A xNA − A + xNA − B + (1 − x) NB − A + (1 − x) NB − B
PB − B =
(1 − x) NB − B + (1 − x) NB − A + (1 − x) NB − B
xNA − A + xNA − B
(1) Fig. 2. Composition dependence of atomic bond percentages of binary Zr–Cu MGs.
(2) PA − B =
xNA − B + (1 − x) NB − A xNA − A + xNA − B + (1 − x) NB − A + (1 − x) NB − B
(3)
where PA-A, PB-B, and PA-B represent the percentages of Zr–Zr, Cu– Cu, and Zr–Cu bonds, respectively. Fig. 2 shows the composition dependence of atomic bond percentages of binary Zr–Cu MGs. When the Zr atomic mole fraction increases, the Zr–Zr bond percentage increases monotonously, whereas the Cu–Cu bond percentage decreases. Zr–Cu bond percentage and atomic mole fraction approximately behave parabolically. The location of the maxima is between 40 and 45 at%, instead of corresponding to a Zr concentration of 50 at%. The bond percentages of Zr–Zr and Cu–Cu are roughly equal, when the Zr–Cu bond percentage is maximal. Fig. 3 shows Young's modulus obtained from the stress–strain curves in the illustration as a function of mole fraction of Zr. Young's modulus and atomic mole fraction approximately behave
Fig. 1. Structural models of metallic glasses.
Fig. 3. Young's modulus of binary Zr–Cu MGs as a function of Zr mole fraction. The illustration shows the stress–strain curves for the different compositions.
W. Zhao et al. / Materials Letters 175 (2016) 227–230
parabolically, and the maxima location shifts to lower Zr mole fraction. The Young's modulus E of binary Zr–Cu MGs can be expressed as:
E = PA − A × E1 + PA − B × E2 + PB − B × E3
(4)
where E1, E2, and E3 are the Young's modulus, which correspond to Zr–Zr, Zr–Cu, and Cu–Cu bonds, respectively. The data in Figs. 2 and 3 can fit well into Eq. (4). The Young's modulus, which corresponds to the Zr–Zr and Cu–Cu bonds, are 61.5 and 82.1 GPa, respectively. These results considerably coincide with the previous work, which reported that the elastic modulus of the amorphous phase is about 30% lower than that of the corresponding crystalline phase [12]. The Young's modulus that corresponds to Zr–Cu bonds is 102.2 GPa, which is greater than that of the Zr–Zr and Cu– Cu bonds. This result is due to the large negative mixing enthalpy between Zr and Cu, and the stiffness of Zr–Cu bond is greater than that of Zr–Zr and Cu–Cu bonds. Previous studies suggest that bond strength between different elements is always higher than that of bonds between similar elements, and bond strength increases
229
with the absolute value of negative mixing enthalpy [13]. Stiffness is always proportional to the strength for most of metallic bonds, therefore, bond stiffness between different elements is the ignored important factor. Some original confusion can be explained by considering bond stiffness. Fig. 4 shows that the elastic moduli of some MGs are cited from previous studies, and the “rule of mixture” that uses atoms as the components is not established in these cases. From the data in Fig. 4(a) [14], the Young's modulus (E) of (Zr50Cu50)90Al10 is 117.3 GPa, which is higher than that of Zr50Cu50 (100.5 GPa) and Al (70 GPa). The Young's modulus of (Zr50Cu50)100 xAlx (x ¼3, 4, 6, 7, 8, and 10 at%) increases from 100.5 to 117.3 GPa when Al content increases from 0 at% to 10 at%. This result suggests that (Zr50Cu50)90Al10 does not inherit its elastic modulus from a single component. With the addition of Al, a large number of Zr–Al bonds form in the MGs. The mixing enthalpy of Zr and Al is 44 kJ/mol, the absolute value of which is higher than that of the mixing enthalpy of Zr and Cu ( 23 kJ/mol). This result suggests that the stiffness of Zr–Al bond is higher than that of Zr–
Fig. 4. Young's modulus of some MGs that are cited from previous studies.
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W. Zhao et al. / Materials Letters 175 (2016) 227–230
Cu bond. Therefore, the elastic modulus of MGs reflects the inherent stiffness of their atomic bonds. Other examples exist, wherein the total elastic modulus increases with the addition of the elements with low elastic modulus. When the Ni (200 GPa) and Cu (130 GPa) in Pr55Cu17Ni8Al20 and Pr60Cu20Ni10Al10 are replaced by Al (70 GPa) with lower elastic modulus, the total elastic modulus increase obviously (Fig. 4(b) and (c)) [7,15]. This phenomenon is due to the higher stiffness of Pr–Al bonds (mixing enthalpy 38 kJ/mol) than that of Pr–Ni ( 30 kJ/mol) and Pr–Cu bonds ( 22 kJ/mol). When the Fe (211 GPa) in Zr45Nb8Cu13Ni4Be22Fe8 is replaced by Nb (105 GPa) and Ni (200 GPa) with lower elastic modulus, the total elastic modulus increase obviously (Fig. 4(d)) [12], because the stiffness of Zr–Ni bonds ( 49 kJ/mol) is higher than that of Zr–Fe bonds ( 25 kJ/ mol). When the Zr (68 GPa) and Co (209 GPa) in Tm40Zr15Al25Co20 are replaced by Y (64 GPa) and Ni (200 GPa) with lower elastic modulus, the total elastic modulus also increase obviously (Fig. 4 (e)) [16], because the stiffness of Tm–Ni bonds ( 34 kJ/mol) is higher than that of Tm–Co bonds ( 24 kJ/mol). The elastic modulus of pure metals is cited in Ref. [12], and the mixing enthalpy is cited in Ref. [17].
macroscopic performance, and will play a huge role in the future research works.
4. Conclusions
[8] [9] [10] [11]
In summary, despite the chemical and structural complexity of the MGs, the stiffness of their atomic bonds is essentially responsible for their elasticity. The “rule of mixture” that uses atomic bonds is more applicable than the use of atoms as the components to explain the inheritance of elastic modulus. The percentage of atomic bonds in metallic glasses can be considered as a microscopic structure parameter which is closely related to the
Acknowledgments This work was supported by the National Natural Science Foundation of China No. 51401104, the Natural Science Foundation of Jiangsu Province No. BK20140765, the Opening Project of Jiangsu Key Laboratory of Advanced Structural Materials and Application Technology (ASMA201417), and Scientific Foundation of Nanjing Institute of Technology (CKJA201503 and YKJ201404).
References [1] [2] [3] [4] [5] [6] [7]
[12] [13] [14] [15] [16] [17]
W. Klement, R.H. Willens, P. Duwez, Nature 187 (1960) 869–870. A. Inoue, Acta Mater. 48 (2000) 279–306. W.H. Wang, Adv. Mater. 21 (2009) 4524–4544. W.H. Wang, Q. Wei, S. Friedrich, Phys. Rev. B 57 (1998) 8211. A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. W.H. Wang, J. Appl. Phys. 99 (2006) 093506. Z.F. Zhao, P. Wen, R.J. Wang, D.Q. Zhao, M.X. Pan, W.H. Wang, J. Mater. Res. 21 (2006) 369–374. M.I.J. Mendelev, Appl. Phys. 102 (2007) 043501. S. Plimpton, J. Comput. Phys. 117 (1995) 1–19. B.I. Yakobson, C.J. Brabec, J. Bernholc, Phys. Rev. Lett. 76 (1996) 2511–2514. W. Zhao, G. Li, Y.Y. Wang, S.D. Feng, L. Qi, M.Z. Ma, R.P. Liu, Mater. Des. 65 (2015) 1048–1052. W.H. Wang, Prog. Mater. Sci. 57 (2012) 487–656. D. Ma, Phys. Rev. Lett. 108 (2012) 085501. T.L. Cheung, C.H. Shek, J. Alloy. Compd. 434–435 (2007) 71–74. Z.F. Zhao, Z. Zhang, P. Wen, M.X. Pan, D.Q. Zhao, W.H. Wang, W.L. Wang, Appl. Phys. Lett. 82 (2003) 4699. H.B. Yu, P. Yu, W.H. Wang, H.Y. Bai, Appl. Phys. Lett. 92 (2008) 141906. A. Takeuchi, A. Inoue, Mater. Trans. 46 (2005) 2817–2829.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Intrinsic correlation between elastic modulus and atomic bond stiffness in metallic glasses W. Zhao a,b, J.L. Cheng a,b, S.D. Feng c, G. Li c, R.P. Liu c,n a
School of Materials Science and Engineering, Nanjing Institute of Technology, Nanjing 211167, China Jiangsu Key Laboratory of Advanced Structural Materials and Application Technology, Nanjing 211167, China c State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 October 2015 Received in revised form 8 February 2016 Accepted 6 March 2016 Available online 8 March 2016
ZrxCu100 x (x ¼15–70) metallic glass (MG) models were constructed by molecular dynamics simulations to explore the intrinsic correlation between elastic modulus and atomic bond stiffness in MGs. The elastic modulus and atomic mole fraction of MGs approximately behave parabolically, and their maxima location shifts to lower Zr mole fraction. This phenomenon is due to the variation of their atomic bond percentages, which suggests that elastic modulus reflects the inherent stiffness of atomic bonds. The “rule of mixture”, which uses atomic bonds as the components, is more applicable than that in which atoms are used as the components to explain the inheritance of elastic modulus. & 2016 Elsevier B.V. All rights reserved.
Keywords: Atomic bond Elastic properties Amorphous materials Molecular dynamics simulation
1. Introduction The disordered atomic structure of metallic glasses (MGs) gives rise to their unique mechanical and physical properties, such as strength and elasticity, and this structure is considered for a wide range of applications [1–5]. Thus, the underlying mechanisms for the mechanical properties of MGs are fundamentally interesting. The development of MGs with efficient structure-property relationship is challenged by the complexity and uncertainty of their structure. To predict MG properties, the previous studies [6,7] achieved remarkable results in estimating elastic modulus by conducting weighted average on the elastic modulus of pure metal, that is, M = ∑ fi Mi , where M represents Young's modulus (E) or shear modulus (G), fi is the atomic fraction of the ith component, and Mi is E or G of the ith component. However, this method can hardly explains certain phenomena, such as the non-monotonic increase in the elastic modulus of Zr–Cu system with the increasing Cu element. The Young's modulus of pure Zr is 68 GPa, and that of pure Cu is 130 GPa [6]. Several important factors are neglected, and thus the unknown important factors should be explored to understand and control these properties. The macroscopic properties of a material are determined by atomic interaction in most cases, including selection of MGs. By using the atomic n
Corresponding author. E-mail address: [email protected] (R.P. Liu).
http://dx.doi.org/10.1016/j.matlet.2016.03.037 0167-577X/& 2016 Elsevier B.V. All rights reserved.
bond as the component and by utilizing the weighted average method (rule of mixture), the present work studies the elastic modulus of Zr–Cu MGs by molecular dynamics simulation, and this new “rule of mixture” can clarify the unexplained problems.
2. Simulation methods ZrxCu100 x MG models with x values of 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, and 70 were prepared. The simulations are performed by using the embedded atom method (EAM) potential [8], which is supplied in LAMMPS [9]. The dimension of the model structures, which are used in the calculations, are 17.1 nm 25.6 nm 4.3 nm in the x, y, and z directions, respectively. The model is heated from 300 K to 2500 K at a constant rate of 10 K/ps. To make the system in a natural state, we relax the liquid system for 50 ps at 2500 K within the NPT ensemble (namely constant number, constant pressure, and constant temperature) under periodic boundary condition by conjugated gradient method [10]. Subsequently, we cool the system from 2500 K to 100 K in 100 K decrements at a constant quenching rate of 5 K/ ps and zero external pressure. The temperature was controlled by Nose–Hoover thermostat method. To annihilate the defects in the models, 5 GPa hydrostatic pressure was initially applied to the models. Then, the atomic bond proportions and elastic modulus were estimated by partial coordination number and stress–strain curve analyses, respectively.
228
W. Zhao et al. / Materials Letters 175 (2016) 227–230
3. Results and discussion Atoms are regarded as the elementary units of MGs in previous studies (Fig. 1(a)), whereas atomic bonds are considered as the elementary units of MGs in the current study (Fig. 1(b)). To apply the “rule of mixture” by using the atomic bonds as the components, the percentages of the different bonds in the Zr–Cu system should be calculated. Atomic bond proportion is a totally new parameter that can be calculated through the average partial coordination number and atomic mole fraction [11]. The total number of atoms in the Zr–Cu system is N, and the number of Zr atoms is xN, where x is the mole fraction of Zr. The number of Zr– Zr bonds can be expressed as xNNA-A/2, where NA-A is the Zr–Zr partial coordination number. Similarly, the number of Cu–Cu bonds can be expressed as (1 x)NNB-B/2, where NB-B is the Cu–Cu partial coordination number. The number of Zr–Cu bonds can be expressed as (xNNA-B þ(1 x)NNB-A)/2, where NA-B is the Zr–Cu partial coordination number, and NB-A is the Cu–Zr partial coordination number. Thus, the atomic bond proportion can be expressed as:
PA − A =
xNA − A xNA − A + xNA − B + (1 − x) NB − A + (1 − x) NB − B
PB − B =
(1 − x) NB − B + (1 − x) NB − A + (1 − x) NB − B
xNA − A + xNA − B
(1) Fig. 2. Composition dependence of atomic bond percentages of binary Zr–Cu MGs.
(2) PA − B =
xNA − B + (1 − x) NB − A xNA − A + xNA − B + (1 − x) NB − A + (1 − x) NB − B
(3)
where PA-A, PB-B, and PA-B represent the percentages of Zr–Zr, Cu– Cu, and Zr–Cu bonds, respectively. Fig. 2 shows the composition dependence of atomic bond percentages of binary Zr–Cu MGs. When the Zr atomic mole fraction increases, the Zr–Zr bond percentage increases monotonously, whereas the Cu–Cu bond percentage decreases. Zr–Cu bond percentage and atomic mole fraction approximately behave parabolically. The location of the maxima is between 40 and 45 at%, instead of corresponding to a Zr concentration of 50 at%. The bond percentages of Zr–Zr and Cu–Cu are roughly equal, when the Zr–Cu bond percentage is maximal. Fig. 3 shows Young's modulus obtained from the stress–strain curves in the illustration as a function of mole fraction of Zr. Young's modulus and atomic mole fraction approximately behave
Fig. 1. Structural models of metallic glasses.
Fig. 3. Young's modulus of binary Zr–Cu MGs as a function of Zr mole fraction. The illustration shows the stress–strain curves for the different compositions.
W. Zhao et al. / Materials Letters 175 (2016) 227–230
parabolically, and the maxima location shifts to lower Zr mole fraction. The Young's modulus E of binary Zr–Cu MGs can be expressed as:
E = PA − A × E1 + PA − B × E2 + PB − B × E3
(4)
where E1, E2, and E3 are the Young's modulus, which correspond to Zr–Zr, Zr–Cu, and Cu–Cu bonds, respectively. The data in Figs. 2 and 3 can fit well into Eq. (4). The Young's modulus, which corresponds to the Zr–Zr and Cu–Cu bonds, are 61.5 and 82.1 GPa, respectively. These results considerably coincide with the previous work, which reported that the elastic modulus of the amorphous phase is about 30% lower than that of the corresponding crystalline phase [12]. The Young's modulus that corresponds to Zr–Cu bonds is 102.2 GPa, which is greater than that of the Zr–Zr and Cu– Cu bonds. This result is due to the large negative mixing enthalpy between Zr and Cu, and the stiffness of Zr–Cu bond is greater than that of Zr–Zr and Cu–Cu bonds. Previous studies suggest that bond strength between different elements is always higher than that of bonds between similar elements, and bond strength increases
229
with the absolute value of negative mixing enthalpy [13]. Stiffness is always proportional to the strength for most of metallic bonds, therefore, bond stiffness between different elements is the ignored important factor. Some original confusion can be explained by considering bond stiffness. Fig. 4 shows that the elastic moduli of some MGs are cited from previous studies, and the “rule of mixture” that uses atoms as the components is not established in these cases. From the data in Fig. 4(a) [14], the Young's modulus (E) of (Zr50Cu50)90Al10 is 117.3 GPa, which is higher than that of Zr50Cu50 (100.5 GPa) and Al (70 GPa). The Young's modulus of (Zr50Cu50)100 xAlx (x ¼3, 4, 6, 7, 8, and 10 at%) increases from 100.5 to 117.3 GPa when Al content increases from 0 at% to 10 at%. This result suggests that (Zr50Cu50)90Al10 does not inherit its elastic modulus from a single component. With the addition of Al, a large number of Zr–Al bonds form in the MGs. The mixing enthalpy of Zr and Al is 44 kJ/mol, the absolute value of which is higher than that of the mixing enthalpy of Zr and Cu ( 23 kJ/mol). This result suggests that the stiffness of Zr–Al bond is higher than that of Zr–
Fig. 4. Young's modulus of some MGs that are cited from previous studies.
230
W. Zhao et al. / Materials Letters 175 (2016) 227–230
Cu bond. Therefore, the elastic modulus of MGs reflects the inherent stiffness of their atomic bonds. Other examples exist, wherein the total elastic modulus increases with the addition of the elements with low elastic modulus. When the Ni (200 GPa) and Cu (130 GPa) in Pr55Cu17Ni8Al20 and Pr60Cu20Ni10Al10 are replaced by Al (70 GPa) with lower elastic modulus, the total elastic modulus increase obviously (Fig. 4(b) and (c)) [7,15]. This phenomenon is due to the higher stiffness of Pr–Al bonds (mixing enthalpy 38 kJ/mol) than that of Pr–Ni ( 30 kJ/mol) and Pr–Cu bonds ( 22 kJ/mol). When the Fe (211 GPa) in Zr45Nb8Cu13Ni4Be22Fe8 is replaced by Nb (105 GPa) and Ni (200 GPa) with lower elastic modulus, the total elastic modulus increase obviously (Fig. 4(d)) [12], because the stiffness of Zr–Ni bonds ( 49 kJ/mol) is higher than that of Zr–Fe bonds ( 25 kJ/ mol). When the Zr (68 GPa) and Co (209 GPa) in Tm40Zr15Al25Co20 are replaced by Y (64 GPa) and Ni (200 GPa) with lower elastic modulus, the total elastic modulus also increase obviously (Fig. 4 (e)) [16], because the stiffness of Tm–Ni bonds ( 34 kJ/mol) is higher than that of Tm–Co bonds ( 24 kJ/mol). The elastic modulus of pure metals is cited in Ref. [12], and the mixing enthalpy is cited in Ref. [17].
macroscopic performance, and will play a huge role in the future research works.
4. Conclusions
[8] [9] [10] [11]
In summary, despite the chemical and structural complexity of the MGs, the stiffness of their atomic bonds is essentially responsible for their elasticity. The “rule of mixture” that uses atomic bonds is more applicable than the use of atoms as the components to explain the inheritance of elastic modulus. The percentage of atomic bonds in metallic glasses can be considered as a microscopic structure parameter which is closely related to the
Acknowledgments This work was supported by the National Natural Science Foundation of China No. 51401104, the Natural Science Foundation of Jiangsu Province No. BK20140765, the Opening Project of Jiangsu Key Laboratory of Advanced Structural Materials and Application Technology (ASMA201417), and Scientific Foundation of Nanjing Institute of Technology (CKJA201503 and YKJ201404).
References [1] [2] [3] [4] [5] [6] [7]
[12] [13] [14] [15] [16] [17]
W. Klement, R.H. Willens, P. Duwez, Nature 187 (1960) 869–870. A. Inoue, Acta Mater. 48 (2000) 279–306. W.H. Wang, Adv. Mater. 21 (2009) 4524–4544. W.H. Wang, Q. Wei, S. Friedrich, Phys. Rev. B 57 (1998) 8211. A. Peker, W.L. Johnson, Appl. Phys. Lett. 63 (1993) 2342. W.H. Wang, J. Appl. Phys. 99 (2006) 093506. Z.F. Zhao, P. Wen, R.J. Wang, D.Q. Zhao, M.X. Pan, W.H. Wang, J. Mater. Res. 21 (2006) 369–374. M.I.J. Mendelev, Appl. Phys. 102 (2007) 043501. S. Plimpton, J. Comput. Phys. 117 (1995) 1–19. B.I. Yakobson, C.J. Brabec, J. Bernholc, Phys. Rev. Lett. 76 (1996) 2511–2514. W. Zhao, G. Li, Y.Y. Wang, S.D. Feng, L. Qi, M.Z. Ma, R.P. Liu, Mater. Des. 65 (2015) 1048–1052. W.H. Wang, Prog. Mater. Sci. 57 (2012) 487–656. D. Ma, Phys. Rev. Lett. 108 (2012) 085501. T.L. Cheung, C.H. Shek, J. Alloy. Compd. 434–435 (2007) 71–74. Z.F. Zhao, Z. Zhang, P. Wen, M.X. Pan, D.Q. Zhao, W.H. Wang, W.L. Wang, Appl. Phys. Lett. 82 (2003) 4699. H.B. Yu, P. Yu, W.H. Wang, H.Y. Bai, Appl. Phys. Lett. 92 (2008) 141906. A. Takeuchi, A. Inoue, Mater. Trans. 46 (2005) 2817–2829.