Diffusivities and atomic mobilities for fcc Cu–Ni–Sn alloys

Calphad 59 (2017) 84–89

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Diffusivities and atomic mobilities for fcc Cu–Ni–Sn alloys a

b

c

a,⁎

a,⁎

MARK d

Yuling Liu , Chong Chen , Dandan Liu , Yong Du , Shuhong Liu , Xiaoma Tao , Yifang Ouyangd a

State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan 410083, China Henan Key Laboratory of High-temperature Structural and Functional Materials, Henan University of Science and Technology, Luoyang, Henan 471023, China Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China d College of Physical Science and Technology, Guangxi University, Nanning, Guangxi 530004, China b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Atomic mobility fcc Cu–Ni–Sn alloys Diffusion couples Interdiffusion coefficients

Utilizing five groups of bulk diffusion couples together with electron probe microanalysis technique, the composition-dependent ternary interdiffusion coefficients in fcc Cu–Ni–Sn alloys at 1023 K were determined via the Whittle and Green method. The presently obtained interdiffusion coefficients at 1023 K as well as our previously measured ones at 1073 K were combined with the slightly modified thermodynamic descriptions of the fcc Cu–Ni–Sn phase to explore atomic mobilities of Cu, Ni and Sn in fcc Cu–Ni–Sn alloys within the CALPHAD framework. In order to be consistent with the thermodynamic description, atomic mobilities in binary fcc Ni–Sn alloys were re-evaluated in the present work. The quality of the assessed kinetic characteristics was confirmed by the comprehensive comparisons between various model-predicted diffusion behaviors and the experimental ones, including concentration profiles and diffusion paths.

1. Introduction As a typical high strength and high elasticity Cu-based material, Cu–Ni–Sn alloys have been widely used owing to their outstanding strength, excellent elasticity, high thermal and electrical conductivity [1–3]. These properties of Cu–Ni–Sn alloys can be remarkably optimized by heat treatment, during which diffusion plays a key role. In addition, the development of new lead-free solders has become a research focus and Sn-based solder alloys are of great concern [4–6]. The interdiffusion reaction between Sn-based solder alloys and metal substrates containing Cu and Ni greatly affects the microstructure in the welding region and thus the properties of the solder. Therefore, a comprehensive understanding of the diffusion behavior in the Cu–Ni–Sn system is extremely important to improve the performance of both Cu-based alloys and Sn-based solders. Such a behavior can be effectively predicted by using DIffusion-Controlled TRAnsformations (DICTRA) software package with the atomic mobility database combined with the thermodynamic database. So far, the thermodynamic description for the Cu–Ni–Sn system has already been constructed by Miettinen [7] and was used in this work. The atomic mobilities in binary fcc Cu–Ni [8,9], Cu–Sn [10–12] and Ni–Sn [13] alloys were already provided by the references cited above. However, the atomic mobilities for fcc Cu–Ni–Sn alloys based on the CALculation of PHAse Diagram (CALPHAD) framework are still

⁎

Corresponding author. E-mail addresses: [email protected] (Y. Du), [email protected] (S. Liu).

http://dx.doi.org/10.1016/j.calphad.2017.08.005 Received 2 August 2017; Received in revised form 31 August 2017; Accepted 31 August 2017 0364-5916/ © 2017 Elsevier Ltd. All rights reserved.

unavailable. A succession of pragmatic methods [14–17] to estimate diffusivities along the whole diffusion couple is prone to a large error [18,19]. Determining the composition-dependent interdiffusivities at the intersection point of two diffusion couples is still the most precise way and was chosen by this work. Consequently, the major purposes of the present work are (i) to experimentally measure the interdiffusivities of fcc Cu–Ni–Sn alloys at 1023 K at the intersection point of each two diffusion couples and this experimental part shall be displayed in next Section; (ii) to evaluate the atomic mobilities of Cu, Ni and Sn in fcc Cu–Ni–Sn alloys based on the experimental interdiffusivities from the present work and our previous measurements at 1073 K [20], and (iii) to verify the reliability of the presently obtained atomic mobilities by comprehensively comparing calculated diffusion properties with the corresponding experimental data, including various concentration profiles and diffusion paths in the diffusion couples. Section 3 is going to present the process of evaluation and modeling of ternary diffusivities. The experimental and calculated results will be discussed in Section 4. Finally, the main conclusions are presented in the last Section. 2. Experimental procedure Five Cu–Ni–Sn diffusion couples, as shown in Table 1, were prepared in the following steps. Copper (purity: 99.99 wt%), nickel (purity:

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1 dx +∞ x ∼3 ∼3 dC D11 + D12 2 = [(1 − Y1) ∫−∞ Y1⋅dx + Y1 ∫x (1 − Y1)⋅dx ] dC1 2t dY1 1 dx +∞ x ∼3 ∼3 dC D22 + D21 1 = [(1 − Y2) ∫−∞ Y2⋅dx + Y2 ∫x (1 − Y2)⋅dx ] dC2 2t dY2

Table 1 List of terminal compositions of the diffusion couples in the present work. Couple

Composition (at%)

C1 C2 C3 C4 C5

Cu–7.38Ni/Cu–4.28Sn Cu–3.75Ni/Cu–4.45Sn Cu/Cu–1.88Ni–4.74Sn Cu/Cu–4.42Ni–3.25Sn Cu/Cu–9.18Ni–1.24Sn

(5)

The four interdiffusion coefficients in Eq. (5) are estimated at the common composition of the intersection of the diffusion paths from two diffusion couples. The standard deviation of the interdiffusivities extracted in the current work was determined using the scientific method proposed by Lechelle et al. [25], who considered the error propagation via the following function:

99.99 wt%) and tin (purity: 99.99 wt%) were used as starting materials for pure Cu and alloys with terminal compositions. They were arc melted under an argon atmosphere using a non-reactive W electrode (WKDHL-1, Opto-electronics Co. Ltd., Beijing, China). All the buttons were re-melted five times to guarantee their homogeneity, and the total weight losses after preparation were less than 1%. After that, the samples were machined into blocks of approximate dimensions of 5 × 5 × 10 mm3 with wire-electrode cutting before mechanically removing the surface material. Then these blocks were sealed into an evacuated quartz tubes, and homogenized at 1023 ± 5 K for 60 days in an L4514type diffusion furnace (Qingdao Instrument & Equipment Co., Ltd., China), followed by quenching in water. The polished and cleaned blocks were bounded together by molybdenum wires to form diffusion couples according to the assembly listed in Table 1. These couples were then sealed into quartz tubes and annealed at 1023 K for 144000 s followed by quenching in water. After standard metallographic technique, the concentration profiles of each diffusion couple were determined by using electron probe microanalysis with wavelength dispersive X-ray analyzer (EPMA/WDX) (JXA-8800R, JEOL, Japan). Variations in alloy compositions were determined to be within ± 0.5 at % for each component.

2

u (f (A, B…)) =

⎛ ∂f ⎞ (u (α ))2 ∂α ⎠ α = A, B … ⎝

∑

(6)

where, A and B are the correlation quantities of function f, while u (α ) (α = A, B…) is the uncertainty in the measurements of variable α like concentration. 3.2. Modeling of atomic mobility and diffusivity According to the absolute reaction rate theory, the atomic mobility of element k, Mk , can be divided into a frequency factor Mk0 and an activation enthalpy Qk [26]. Mk can be expressed as [27]:

Mk = exp ⎜⎛ ⎝

RT ln Mk0 ⎞ −Qk ⎞ 1 mg Γ ⎟ exp ⎛ RT ⎝ RT ⎠ RT ⎠

(7) mg

3. Evaluation and modeling of ternary diffusivities

where R is the gas constant and T is the absolute temperature. Γ is a factor taking into account the magnetic contribution to the diffusivity and can be neglected in the fcc phase [28]. Thus, the corresponding atomic mobility parameters in the DICTRA notation, Qk and RT ln Mk0 can be merged into one parameter, i.e. Φk . The composition dependency of Φk can be represented with the Redlich-Kister polynomial [29]:

3.1. Evaluation of ternary interdiffusion coefficients

Φk =

∑ xi Φik + ∑ ∑ xi xj ⎡⎢∑ rΦki,j (xi − xj)r ⎤⎥ i

Taking component 3 as the solvent, the interdiffusion in a fictitious 1–2–3 ternary system can be expressed by an extended Fick's second law on the basis of Matano coordinates [21]:

∂Ci ∂ ⎛ ∼3 ∂C1 ⎞ ∂ ⎛ ∼3 ∂C2 ⎞ = Di1 + Di2 ; (i = 1, 2) ∂t ∂x ⎝ ∂x ⎠ ∂x ⎝ ∂x ⎠

+

C ∫C2−2 xdC2

( ∼ = −2t (D

3 ∂C1 21 ∂x

) )

∼3 ∂C + D22 ∂x2

(1)

s vijk = xs +

Ci − Ci− ; (i = 1, 2) Ci+ − Ci−

(8)

1 − x i − x j − xk 3

;

(s = i, j, k )

(9)

where xs , x i , x j and xk are mole fractions of elements s, i, j and k, respectively. The intrinsic diffusion coefficients with n as the dependent species are correlated to the atomic mobilities by [30]

(2)

I

∂μi ⎞ ∂μ Dijn = x i Mi ⎛⎜ i − ⎟ ∂ ∂ x xn ⎠ ⎝ j

(10)

where μi is the chemical potential of element i. The relation between the inter-diffusion coefficients and the intrinsic coefficients can be given as follows: ∼n Dkj = ∑ (δik − xk ) I Dijn (11) i

(3)

In order to avoid the differences between the locations of Matano plane for solutes 1 and 2, Whittle and Green [24] have suggested to introduce the normalized concentration parameter Yi, where

Yi =

(s = i, j, k )

⎦

s

where x i is the mole fraction of species i, is the value of Φk for pure i and thus represents the value of one endpoint in the composition space. r i, j Φk and sΦki, j, k are binary and ternary interaction parameters to be r evaluated. Each individual Φ parameter, i.e. Φik , Φki, j and sΦki, j, k , can be expressed by a polynomial of temperature and pressure if necessary. s The parameter vijk is given by

Kirkaldy et al. [22,23] have shown that Eq. (1) can be solved by an extension of the Boltzmann-Matano method into a ternary one: C ∼3 ∼3 ∫C1−1 xdC1 = −2t D11 ∂∂Cx1 + D12 ∂∂Cx2

⎣

j>i k>j

Φik

2) 2)

⎦

r

∑ ∑ ∑ xi xj xk ⎡⎢∑ vijks sΦki,j,k⎤⎥; i

where x is the diffusion distance from Matano interface, t represents ∼3 ∼3 time and Ci is concentration of component i. D11 and D22 are the main ∼3 ∼3 interdiffusion coefficients. D12 and D21 are the cross interdiffusion coefficients. For semi-infinite diffusion couples, the initial and boundary conditions are

Ci (−x , 0) = Ci (−∞, t ) = Ci−; (i = 1, Ci (x , 0) = Ci (+∞, t ) = Ci+; (i = 1,

⎣

j>i

i

where δik is the Kronecker delta (δik = 1 if i = k , otherwise δik = 0 ). Assuming the mono-vacancy atomic exchange mechanism, the tracer diffusivity Di* relates to the atomic mobility Mi via the Einstein relation [31]

(4)

Then the ternary interdiffusion coefficients can be determined by solving the following equations: 85

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Table 2 Diffusion coefficients in Cu-rich fcc Cu–Ni–Sn alloys at 1023 K obtained in this work. Diffusion couple

C1/C2 C1/C3 C1/C4 C1/C5 C2/C3 C2/C4 C2/C5 a

Interdiffusion coefficient (× 10−15m2s−1)a

Composition (at%) Ni

Sn

∼Cu D NiNi (SD)

∼Cu D NiSn (SD)

∼Cu DSnNi (SD)

∼Cu DSnSn (SD)

1.56 1.05 4.41 7.35 1.17 3.40 3.74

2.65 2.65 2.81 0.68 2.73 1.92 0.47

3.82 3.39 2.90 1.16 4.61 1.81 1.04

−5.60 ( ± 4.69) −1.07 ( ± 3.15) 0.01 ( ± 2.03) −0.43 ( ± 0.63) −2.62 ( ± 0.22) −3.61 ( ± 0.97) −0.56 ( ± 0.64)

−12.17 ( ± 10.43) −12.84 ( ± 10.27) −7.88 ( ± 8.06) −0.59 ( ± 1.74) −12.84 ( ± 2.02) −4.04 ( ± 2.30) −0.78 ( ± 0.49)

50.95 53.21 24.90 15.71 52.53 39.30 23.52

( ± 2.31) ( ± 2.20) ( ± 0.04) ( ± 0.09) ( ± 0.15) ( ± 0.24) ( ± 0.03)

( ± 25.01) ( ± 16.31) ( ± 4.28) ( ± 8.74) ( ± 2.78) ( ± 10.66) ( ± 9.81)

SD = standard deviation, which was evaluated using the method considering the error propagation [25].

Table 3 Summary of the atomic mobility parameters for fcc Cu–Ni–Sn alloys assessed in the present work as well as those from the literature (all in SI units). Mobility Mobility of Cu

Mobility of Ni

Mobility of Sn

Parameters, J/mol

Reference

ΦCu Cu = − 205872.0 − 82.52 × T

[41]

Ni ΦCu = −263689.7 − 77.04 × T

[9]

Sn ΦCu = −59345 − 85.36 × T

[10]

ΦCu,Ni = 14204.2 − 4.98 × T Cu ΦCu,Sn = 425070.5 Cu ΦCu = − 271377.6 − 81.79 × T Ni ΦNi Ni = − 229936.8 − 72.83 × T ΦCu Ni = − 59345 − 85.36 × T ΦCu,Ni = 39620.8 − 24.19 × T Ni ΦCu,Sn = 710383.1 Ni ΦNi,Sn = 437617.0 − 134.41 × T Ni ΦCu Sn = − 172907 − 91.78 × T Ni ΦSn = −257207.0 − 71.60 × T ΦSn Sn = − 59345 − 85.36 × T ΦCu,Ni = −47693.0 Sn ΦCu,Sn = 30831.5 Sn Ni,Sn ΦSn = −420626.0 + 186.29 × T

[9] [12] [9] [42] [10] [9] This work This work [12]

Fig. 2. Comparison between the model-predicted (denoted in solid lines) and measured [13] concentration profiles of Ni/Ni–7.3Sn (at%) diffusion couples annealed at 1173 K for 1512000 s, 1223 K for 1296000 s, 1273 K for 950400 s and 1323 K for 648000 s, respectively. The model-predicted results (denoted in dash lines) due to the previous assessment [13] are also superimposed. The concentration profiles at 1223, 1273 and 1323 K are respectively moved 600, 1200 and 2000 µm to the right side for visibility.

This work [10] This work [12] This work

Fig. 3. Comparison of the presently calculated main interdiffusion coefficients in fcc Cu–Ni–Sn alloys at 1023 and 1073 K with the experimental values by our previous work [20] and the present work. Dashed lines refer to the diffusion coefficients with a factor of 2 or 0.5 from the model-predicted diffusion coefficients in this work.

Fig. 1. Comparison between the calculated composition-dependent interdiffusion coefficients (denoted in solid lines) in the fcc Ni–Sn alloys at 1223–1473 K and the experimental data [38]. The calculated results (denoted in dash lines) due to the previous assessment [13] are also superimposed.

4. Results and discussion

Di* = RTMi

(12) 4.1. Interdiffusion coefficients at 1023 K The concentration profiles of all the diffusion couples were determined by EPMA. According to our previous investigation on fitting 86

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Fig. 4. Model-predicted concentration profiles of Ni and Sn in the fcc Cu–Ni–Sn alloys, compared with the data measured in diffusion couples of (a) Cu–7.38Ni/Cu–4.28Sn, (b) Cu–3.75Ni/Cu–4.45Sn, (c) Cu/Cu–1.88Ni–4.74Sn, (d) Cu/Cu–4.42Ni–3.25Sn and (e) Cu/Cu–9.18Ni–1.24Sn (at%) at 1023 K for 144,000 s in the present work.

experimental data at 1023 K in this work and 1073 K in our previous work [20]. The thermodynamic description of the Cu–Ni–Sn ternary system at Cu–Ni side was evaluated by Miettinen [7] and these parameters were adopted in the present work. Considering the consistence with the multi-component thermodynamic database for light alloys [34], a modification was made that the well-established thermodynamic parameters of the Cu–Ni system assessed by Mey [35] were used instead of that utilized in ref. [7]. The comparisons between the calculated results using the present thermodynamic parameters and the parameters from Miettinen [7] show a good agreement and indicate that the modification is reliable. The atomic mobilities in fcc Cu–Ni alloys were taken from the recent assessment work by Zhang et al. [9]. Xu et al. [12] and Wang et al. [13] investigated the atomic mobilities in fcc Cu–Sn and fcc Ni–Sn alloys, respectively. However, the thermodynamic parameters adopted by Xu et al. [12] and Wang et al. [13] are different from the parameters used in the present work. The calculated diffusivities using atomic parameters for fcc Ni–Sn alloys [13] coupled with the present thermodynamic description cannot well reproduce the experimental data [13,36–38], while the diffusivities for fcc Cu–Sn alloys can well reproduce the experimental data. Therefore, the atomic parameters for fcc Ni–Sn alloys were re-evaluated and those for fcc Cu–Sn alloys in ref. [12] are adopted. The finally obtained atomic mobility parameters for fcc Cu–Ni–Sn alloys, as well as those in boundary binaries from the literature and the present work, are listed in Table 3. A few typical results are displayed to demonstrate the reliability of the atomic mobilities in fcc Ni–Sn alloys obtained in this work. Fig. 1 presents a comparison between the presently calculated interdiffusivities and the experimental data [38] in fcc Ni–Sn alloys at different temperatures. The model-predicted concentration profiles in Ni/

functions applied to the measured concentration profiles [20], the Boltzmann function and additive Boltzmann function were used to fit the presently measured concentration profiles of Ni and Sn, respectively. ∼Cu ∼Cu ∼Cu ∼Cu The interdiffusion coefficients DNiNi , DSnSn , DSnNi and DNiSn were determined at the intersection compositions of the diffusion paths using Eqs. (4) and (5). The currently obtained diffusion coefficients by the Whittle and Green method [24] are listed in Table 2, together with the corresponding standard deviation (SD). As can be seen in the table, the ∼Cu values of the main interdiffusion coefficients DSnSn are almost larger Cu Cu ∼ ∼ than DNiNi by one order of magnitude and DSnNi are negative at 1023 K, which are similar to those at 1073 K [20]. To further validate the reliability of the presently obtained interdiffusion coefficients, they were examined by the following constraints, which guarantee the stability of the solid solution [32]

∼Cu ∼Cu DNiNi + DSnSn > 0 ∼Cu ∼Cu ∼Cu ∼Cu DNiNi⋅DSnSn − DNiSn⋅DSnNi ≥ 0 ∼Cu ∼Cu 2 ∼Cu ∼Cu (DNiNi − DSnSn ) + 4⋅DNiSn⋅DSnNi ≥ 0

(13)

Substituting the determined interdiffusion coefficients into Eq. (13), it was found that all of them fulfill these constraints. Therefore, it can be concluded that the presently obtained interdiffusion coefficients are reliable. 4.2. Assessment of atomic mobilities The atomic mobilities for the fcc Cu–Ni–Sn alloys were assessed by the PARROT module of the DICTRA software [33] based on all the 87

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Fig. 5. Model-predicted concentration profiles of Ni and Sn in the fcc Cu–Ni–Sn alloys, compared with the data measured in diffusion couples of (a) Cu–6.95Ni/Cu–4.58Sn, (b) Cu–3.48Ni/Cu–4.49Sn, (c) Cu–7.14Ni/Cu–2.31Sn, (d) Cu–3.54Ni/Cu–2.25Sn, (e) Cu/Cu–4.06Ni–2.83Sn and (f) Cu/Cu–9.11Ni–1.40Sn (at%) at 1073 K for 129,600 s in our previous work [20].

Fig. 6. Comparison between the model-predicted and experimentally measured diffusion paths of fcc Cu–Ni–Sn alloys at (a) 1023 K for 144,000 s in this work and (b) 1073 K for 129,600 s in ref. [20].

obtained atomic mobilities are compared with the experimental measured data in ref. [20] and this work, as schematically presented in Fig. 3. The dashed lines, which refer to the diffusivities with a differential factor of 2 or 0.5 from the calculated ones, are also superimposed in the plot. It can be seen from these results that nearly all the experimental data were within this general error range. Furthermore, based on the presently evaluated atomic mobilities together with the thermodynamic description, the concentration profiles and diffusion paths in various diffusion couples are model-predicted. This type of simulation is also an effective way to verify the

Ni–7.3 at% Sn diffusion couples at 1173, 1223, 1273 and 1323 K are shown in Fig. 2 and compared with those from the experimental determinations [13]. The calculated results using the atomic mobilities assessed by Wang et al. [13] are also included in Figs. 1 and 2 for a direct comparison. As can be seen in the figures, the re-evaluated atomic mobilities for fcc Ni–Sn alloys in accordance with the present thermodynamic parameters provide an improved agreement to the experimental results [13,38]. ∼Cu ∼Cu The calculated main interdiffusion coefficients DNiNi and DSnSn in the fcc Cu–Ni–Sn alloys at 1023 and 1073 K based on the presently 88

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reliability of the obtained atomic mobilities. Figs. 4 and 5 present the model-predicted concentration-distance profiles for different diffusion couples annealed at 1023 K for 144,000 s compared with the measured data in this work and at 1073 K for 129,600 s compared with the measured data in our previous work [20], respectively. As can be seen in the figures, the agreement between the model-predicted concentration profiles and the experimental data is generally good. It is worth mentioning that the complex features including a change of sign for the slope of the tangent line in the measured Sn concentration profile can be also well reproduced by the present calculations. These complex features are caused by the accumulation of Sn in the interface of Cu–Ni binary alloy which illustrate that Sn diffuses faster than Ni and Ni can effectively impede the diffusion of Sn. The model-predicted diffusion paths for the 5 ternary diffusion couples annealed at 1023 K for 144,000 s in this work and 6 diffusion couples annealed at 1073 K for 129,600 s in ref. [20] are compared with the measured ones in Fig. 6. It can be seen that the presently obtained atomic mobilities can give an accurate prediction of diffusion paths for all diffusion couples, which again indicates the reliability of the presently obtained atomic mobilities at 1023 and 1073 K. The atomic mobilities of all the binary systems have been constructed based on a large amount of experimental data in wide composition and temperature ranges. For example, the atomic mobilities of the fcc Cu-Ni [8,9], Cu–Sn [10–12] and Ni–Sn [13] alloys were assessed based on the experimental investigation inside the experimental ranges of 973–1630, 873–1345 and 1173–1642 K, respectively. The obtained kinetic description for fcc Cu–Ni–Sn alloys is expected to be valid in the Cu-rich fcc Cu–Ni–Sn alloys from about 973–1357 K (melting point of Cu). According to the Arrhenius equation and the well-constructed atomic mobilities of binary systems, the atomic mobilities of the fcc Cu–Ni–Sn alloys also can provide fruitful information at other temperatures and composition regions. And this description has been incorporated into the atomic mobilities database [39,40]. 5. Conclusions A series of ternary fcc/fcc-type diffusion couples was designed in the present work to determine the interdiffusion coefficients in fcc Cu–Ni–Sn alloys at 1023 K using EPMA technique and Whittle and Green method. Based on the measured interdiffusion coefficients at 1023 K and our previous work at 1073 K coupled with the slightly modified thermodynamic description, atomic mobilities of Cu, Ni and Sn in fcc Cu–Ni–Sn alloys were evaluated with the CALPHAD approach. The atomic mobilities of fcc Ni–Sn alloys were re-evaluated to coincide with the present thermodynamic description. Comprehensive comparisons between the model-predicted and the experimentally measured diffusion coefficients, concentration profiles and diffusion paths further verify the reliability of the presently obtained atomic mobilities. Acknowledgements The financial support from National Natural Science Foundation of China (Grant No. 51671219) is greatly acknowledged. References [1] P. Virtanen, T. Tiainen, Stress relaxation behaviour in bending of high strength copper alloys in the Cu–Ni–Sn system, Mater. Sci. Eng. A 238 (1997) 407–410. [2] J.T. Plewes, High-strength Cu-Ni-Sn alloys by thermomechanical processing, Metall. Trans. A 6 (1975) 537. [3] S. Cong, F. Han, X. Wang, Heat treatment processes, microstructure and properties of super high strength Cu-Ni-Sn alloy, Jinshu Rechuli 35 (2010) 43–47. [4] M. Abtew, G. Selvaduray, Lead-free solders in microelectronics, Mater. Sci. Eng. R Rep. 27 (2000) 95–141. [5] K. Zeng, K.N. Tu, Six cases of reliability study of Pb-free solder joints in electronic packaging technology, Mat. Sci. Eng. R 38 (2002) 55–105. [6] T. Maeshima, H. Ikehata, K. Terui, Y. Sakamoto, Effect of Ni to the Cu substrate on the interfacial reaction with Sn-Cu solder, Mater. Des. 103 (2016) 106–113. [7] J. Miettinen, Thermodynamic description of the Cu–Ni–Sn system at the Cu–Ni side,

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