Ni–Cu interdiffusion and its implication for ageing in Ni-coated Cu conductors

Materials Science and Engineering B 198 (2015) 86–94

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Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb

Ni–Cu interdiffusion and its implication for ageing in Ni-coated Cu conductors Zijing Wang a , Le Fang b , Ian Cotton b , Robert Freer a,∗ a b

School of Materials, University of Manchester, Manchester M13 9PL, United Kingdom School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL, United Kingdom

a r t i c l e

i n f o

Article history: Received 17 December 2014 Received in revised form 7 April 2015 Accepted 10 April 2015 Available online 24 April 2015 Keywords: Metallic conductor Ni-coated Cu Thermal ageing Electrical resistivity Diffusion Numerical simulation

a b s t r a c t After heat treatment at 400 ◦ C the effective resistivities of typical Ni-coated Cu conductor wires increased by up to 6.9% as a result of Ni–Cu interdiffusion. Direct Ni–Cu interdiffusion experiments were performed between metal foils at temperatures of 400–600 ◦ C for times up to 192 h. Calculated activation energies were in range 80–90 kJ mol−1 , consistent with a grain boundary diffusion mechanism. Analysis of published Ni–Cu interdiffusion coefficients suggested a clear dependence on grain size and grain shape. A concentric circle model was developed to simulate changes in composition and effective resistivity in the Ni–Cu wires as a function of time. It was predicted that it would take 1.4 × 105 h at 400 ◦ C for 10% increase in the effective resistivity of an AWG18-Class27 conductor wire. Good agreement between simulated and experimental data for effective resistivity was only achieved by employing effective diffusion coefficients corrected for microstructural effects. © 2015 Published by Elsevier B.V.

1. Introduction There is growing interest in the use of metal-coated conductors [1–4], such as Cu coated Al wires [5] and Ni coated Cu wires [6], for interconnection applications including power transmissions, electrical interconnections and microcomponent connections, because these conductors offer advantages compared to conventional, single-metal conductors (e.g. Cu and Al). Consisting of a lowresistivity Cu shell and a light weight core of Al, Cu coated Al wires offer a high (electrical) conductivity to weight ratio to the automobile industry. However, the temperature limit of such wires is about 200 ◦ C, beyond which the growth of intermetallic compounds can lead to embrittlement [5]. In addition, high temperature oxidation of Cu limits the use of Cu coated Al wires in future aerospace applications where electrical motors will be required to operate at elevated temperatures (300–500 ◦ C). Since a Ni coating can protect Cu conductors at elevated temperatures, Ni coated Cu wires are preferable for high temperature applications. A primary requirement for any interconnection system to be employed in the next generation of aerospace applications is that it should perform reliably throughout the lifetime of the motor [4]. Therefore, the effects of thermal ageing on the mechanical

∗ Corresponding author. Tel.: +44 1613063564. E-mail address: [email protected] (R. Freer). http://dx.doi.org/10.1016/j.mseb.2015.04.006 0921-5107/© 2015 Published by Elsevier B.V.

and electrical properties of these wires are of great concern to the designers of the electrical motors. Kim et al. [7] showed that the development of intermetallic phases during the ageing of Cu coated Al wires could lead to progressive embrittlement of the conductors at high temperatures [8], and damage to motor components. Unfortunately, the physical processes occurring in composite wire conductors during extended thermal exposure have received comparatively little attention. In the work of Loos and Haar [9], a thin layer of Ni was applied by electroless plating onto the surface of Cu microstrips in order to prevent polymer dielectrics from being contaminated by Cu during the high temperature curing of the polymer materials at 350 ◦ C; they found a measurable increase in the resistance of the Ni-coated Cu microstrips as a result of Ni diffusing into the Cu. There is also evidence that the effective electrical resistivity of Ni–Cu foil sandwich assemblies increases steadily when subjected to high temperature environments [10]. This is consistent with the known behaviour of Ni–Cu alloys, where effective electrical resistivity increases significantly with Ni content. Ho et al. [11] noted that Ni–Cu alloys containing more than 40% Ni exhibit significantly higher resistivity than end member compositions due to short-range clustering. The practical impact of increased electrical resistivity of the wire used in a machine is that the I2 R losses may increase with time, degrading the performance of the electrical system. Thus Ni–Cu interdiffusion processes need to be understood in order to predict the long-term behaviour of the conductors and the aerospace or other systems in which they are used.

Z. Wang et al. / Materials Science and Engineering B 198 (2015) 86–94 Table 1 AWG20-Class3 and AWG18-Class 27 wires used in ageing experiments. Wire

Diameter (mm)

Ni coating thickness (␮m)

AWG20-Class 3 AWG18-Class27

0.81 1.02

6.1 74

87

per hour. From the total resistance of the wire (R), the effective resistivity () could be determined in the usual way from Eq. (1). =R

A l

(1)

where A is the cross-sectional area of the wire of length l. 2.2. Microstructural examination

Diffusion in the Ni–Cu binary system has been extensively studied using a variety of geometries and temperature ranges [12–16]. Whilst there is broad agreement between the published data, there are clear differences relating to materials used and experimental configurations. Hart [17] suggested that microstructural factors including grain size and morphological parameters could govern diffusion processes at low and intermediate temperatures [18]. In view of the variation in published Ni–Cu diffusivity values, it is essential to take into account microstructural and related factors to ensure the diffusion data is appropriate for individual materials and specific engineering applications. The objectives of the present study are to investigate (i) the effective resistivity of typical Ni coated Cu conductors at elevated temperature, (ii) Ni–Cu interdiffusion processes and their behaviour under conditions relevant to Cu conductor performance, and (iii) to develop a diffusion-based model to predict the long-term electrical properties of Ni-coated conductors at high temperatures.

2. Materials and methods 2.1. Ageing experiments for Ni-coated Cu wires The wires selected for investigation were obtained from Compagnie Générale des Plastiques (France). The wires are typical AWG20-CLASS3 and AWG18-Class27 Ni coated Cu wires in accordance with ASTM standard B355 [19]; details of the wires are presented in Table 1. Typically, very thin (<10 ␮m) coating of Ni on the surface of Cu conductor AWG20-Class3 wires are applied by conventional electroplating methods [20], whilst hot-cladding methods are often used to apply thicker (>70 ␮m) Ni coatings on AWG18-Class27 wires. Sections of the as-received wire 4 m long were wound round alumina tubes 50 mm diameter, to produce coils approximately 50 mm long. These were placed in a Vecstar Muffle Furnace and heated continuously at 400 ◦ C for times up to 5500 h. Outside the furnace the wires were connected to a Keithey 65515 Micro-ohmmeter and a data logger to enable the resistance of the wire to be recorded once

Small fractions of as-received AWG20-Class3 and AWG18Class27 wires and samples thermally aged at 400 ◦ C for periods of 600 h or 1200 h were cut and mounted in epoxy resin. The cross-sections of the wires were ground on SiC papers to 1200 grade and polished down to 1 ␮m diamond paste and finally with colloidal silica suspension. After carbon coating, the morphologies were examined in detail using Philips XL30 and Zeiss EVO 60 Scanning Electron Microscopes; compositional variation across Ni–Cu surface region was investigated by Energy Dispersive Spectroscopy (EDS) techniques. To aid microstructural investigations, selected samples were etched for 5 s in an ethanol based solution containing 20 vol% HCl and 5 wt% FeCl3 ; the average grain sizes of the wires were determined by the linear intercept method [21]. 2.3. Ni–Cu interdiffusion experiments Ni–Cu interdiffusion couples were prepared as Ni–Cu–Ni assemblies using high purity Ni and Cu foils (0.5 mm thick, 99.95%, Alfa Aesar). The foils were cut into squares of side 10 mm, polished down to 0.25 ␮m diamond paste, cleaned in acetone and dried. The Ni–Cu–Ni foils were stacked together and placed between a pair of alumina plates and held in close contact by alumina screws. The diffusion couples were annealed at temperatures in the range 400–600 ◦ C for periods of 48–192 h. All experiments were performed in flowing argon in a Vecstar VTF-7 tube furnace, using a heating rate and cooling rate of 5 ◦ C/min. After cooling, metallurgical cross-sections of the annealed Ni–Cu diffusion couples were prepared. The variation in Ni and Cu concentrations across the interfaces was determined by use of a Philips XL30 SEM equipped with EDS; Ni and Cu concentrations were obtained at 2 ␮m intervals. At least five compositional profiles were collected for each sample interface. 3. Results and discussion 3.1. Morphology of as-received Ni-coated Cu wires Optical micrographs for cross-sections of etched, as-received AWG20-Class3 and AWG18-Class27 Ni-coated Cu wires are

Fig. 1. Optical micrographs (etched surfaces) of as-received wires: (a) AWG20-Class3 wire and (b) AWG18-Class27 Ni-coated Cu wire.

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Fig. 2. Effective resistivities of AWG20-Class3 () and AWG18-Class27 ( coated Cu wires as a function of ageing time at 400 ◦ C.

) Ni

presented in Fig. 1. From the micrographs, the Ni coating thickness was found to be 6 ␮m for AWG20-Class3 and 75 ␮m for AWG18Class27 wire, consistent with ASTM standard B355 [19]. The grain morphology of the Cu core of the AWG20-Class3 wire is characterized by small uniform grains, and a mixture of hexagonal and elongated grains; with average grain size of 7 ␮m. In contrast there were large, elongated 100 ␮m grains in the Cu core of the AWG18Class27 wires. 3.2. Ageing experiments for Ni-coated Cu wires Fig. 2 shows the effective electrical resistivity at 400 ◦ C, as a function of ageing time, for AWG20-Class3 and AWG18-Class27 Ni coated Cu wires. The effective electrical resistivity of the AWG20Class3 Ni-coated Cu wire annealed at 400 ◦ C gradually increased from 4.26 × 10−8 to 4.60 × 10−8  m after 5500 h; in contrast the effective electrical resistivity of the AWG18-Class27 Ni-coated Cu wire increased from 5.58 × 10−8 to 5.70 × 10−8  m after 5500 h. This indicates that effective electrical resistivities of AWG20-Class3 and AWG18-Class27 annealed at 400 ◦ C, increased by 6.9% and 2.3%, respectively. Similarly, when the AWG20-Class3 wire was annealed at 500 ◦ C for 1200 h its effective resistivity increased by 13.5%. Such increases are of potential concern to designers of high temperature electrical systems as it implies that with increasing temperature of operation, there will be an increase in the overall wire resistance, and therefore greater power demands. Understanding the mechanisms of the increase in effective resistivity with ageing is important as it could help to identify routes to minimize its effect. EDS compositional analysis of cross-sections of as-received and heat-treated Ni-coated wires showed marked differences. In the AWG20-Class3 as-received wires there was a clear Ni region, approximately 6 ␮m thick, on the surface of the Cu core, in accordance with the ASTM standard [19]. Analysis of the heat-treated wires indicated that the Ni-rich coatings had reduced in thickness and there was evidence of interdiffusion between Ni and Cu; this increased with annealing time. Even with the thicker coatings on the AWG18-Class27 wire, the short diffusion profiles and curved sample geometry made it impossible to gather statistically reliable compositional profiles for quantitative analysis. These observations indicate that diffusion processes occur upon extended heat treatment. Kim et al. [7] and Gueydan et al. [5] showed that interdiffusion and the development of intermetallic compounds can give rise to changes in both mechanical and electrical properties. Indeed, Ho et al. [11] compiled electrical resistivity data for the Ni–Cu binary

Fig. 3. Optical micrograph of an as-fabricated Ni–Cu diffusion couple.

alloy system as functions of alloy composition and temperature and found that the resistivity of a bulk Ni–Cu alloy varies with its composition in a grossly non-linear way; for example 50–50%, Ni–Cu compositions are significantly more resistive than either of the two end members. According to Ho et al. [11], Ni–Cu alloys do not form complete solid solutions with truly random atomic arrangements; at certain alloy compositions (near to the 50–50% alloy), Ni tends to segregate from Cu and form short-range clusters, thereby causing the resistivity of the alloy to be higher than either of the two end members. In the annealed Ni-coated Cu wires, the migration of Ni into the Cu core led to the formation of a Ni–Cu alloy zone at the Ni–Cu interface with composition gradually changing; this alloy zone should have a much higher resistivity than either pure Ni or Cu. It is then plausible that this alloy zone controlled the overall/effective resistivity of the wire, thus causing an increase in the effective resistivity of the annealed Ni-coated Cu wires. 3.3. Ni–Cu interdiffusion experiments Fig. 3 shows an optical micrograph of a cross-section of an as-fabricated Ni–Cu diffusion couple used for interdiffusion experiments. By chemically etching, the morphology was revealed: uniform and hexagonal-shaped Cu grains were found in the Cu foil used for diffusion experiments. Using the linear intercept method, the average grain size of the Cu was found to be 18 ␮m. After high temperature annealing, EDS compositional profiles were collected for both elements across the metallic interfaces using methods similar to those employed by Arnould and Hild [22]. Although there are significant uncertainties in compositional analyses for very short diffusion lengths, the relative errors decrease and vanish for long diffusion profiles [22]. In the current Ni–Cu diffusion experiments, diffusion lengths of 18–50 ␮m were obtained in all annealed couples. For such long diffusion lengths, a resolution of ±2% can be achieved using EDS techniques [22]. A typical Ni concentration profile is shown in Fig. 4. The central part of the profile, representing the interdiffusion region, is approximately 24 ␮m long. ˜ Ni−Cu The composition-dependent interdiffusion coefficients D were determined by conventional Boltzmann-Matano method [23] using Eq. (2) ˜ (c=c ) = − D

1 2t



 dx  dc

c=c 

c=c 

xdc

(2)

c=0

˜ (c=c ) is the composition-dependent interdiffusion coefwhere D ficient at the concentration of interest, t is the duration of the

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Table 2 Composition-dependent interdiffusion parameters for the Ni–Cu binary system determined in the present study. Ni concentration (%)

Pre-exponential factor (D0 ) (×10−11 m2 s−1 )

Activation energy (Q) (kJ mol−1 )

10 20 30 40 50 60 70 80 90

3.74 3.63 5.23 5.99 7.20 3.76 2.08 1.18 8.86

82 82 86 88 90 87 84 80 79

± ± ± ± ± ± ± ± ±

7 7 6 6 6 7 10 11 14

[14,15,24,25]. Hayashi et al. [15] argued that the Dc (Ni–Cu) interdiffusion data obey Darken’s equation: ˜ c = xCu DNi + xNi DCu D Fig. 4. Typical Ni concentration profile following Ni–Cu interdiffusion in the foils (500 ◦ C for 96 h); Region A: pure Cu; Region B: the interdiffusion region; Region C: pure Ni; the vertical line located at x = 26 ␮m is the Matano Interface.

diffusion anneal (s), (dx/dc)c=c is the inverse concentration gra-

 c=c

dient at concentration c , and c=0 x dc is the integral with respect to the Matano interface (the interface across which there is a zero net mass transport of material), up to the composition of interest c . In the case of the compositional profile shown in Fig. 4, the Matano interface was calculated to be at a location equal to 26 ␮m from the origin of the profile. The vertical line at this location (‘26 ␮m’) ˜ Ni−Cu using Eq. (2) on this comdefines x = 0 for all calculations of D position profile. For each profile, interdiffusion coefficients were calculated in steps of 10 at.% from 10% to 90% Ni for the temperature range 400–600 ◦ C. The composition-dependent Ni–Cu interdiffusion coefficients are presented in Fig. 5. All the data indicate that the interdiffusion coefficient decreases with increasing Ni concentration. This is entirely consistent with earlier investigations of the system which employed different geometries and starting materials

(3)

where xCu and xNi represent the atom fractions of the two species, whilst DNi and DCu are chemical diffusion coefficients for Ni and Cu respectively. Most analyses of the Ni–Cu system have concluded that the chemical diffusion coefficient for Ni exceeds that for Cu by a factor of two [25,26]. Heumann and Grundhof [27] noted that the net effect of this difference was that there would be a Kirkendall effect [28] with the Matano interface moving towards the Cu side of the original junction. Thus with increasing time at elevated temperatures, the Ni coating on the wires will be consumed as interdiffusion progresses [13,14,24,29,30]. The temperature dependence of the interdiffusion coefficients, obtained from the foil experiments (extracted from the compositional dependence data shown in Fig. 5), follow a standard Arrhenius-type relationship:

 Q

˜ (T ) = D0 exp − D

(4)

RT

˜ (T ) is the interdiffusion coefficient at a specific temperature, where D D0 is the pre-exponential factor, Q is the activation energy, R is the gas constant and T is the absolute temperature. The calculated activation energies and D0 values are summarized in Table 2. Whilst the activation energy varies slightly with composition from 79 to 90 kJ mol−1 , the values fall well within the range of published data (Table 3) for temperatures of 200–1050 ◦ C. At the highest temperatures (950–1050 ◦ C), working with single crystals Fisher and Rudman [13] reported a high activation energy of 217.6 kJ mol−1 . Schwarz et al. [24] found a similar value (225 kJ mol−1 ) at temperatures of 500–650 ◦ C and attributed the high activation energy to a vacancy/lattice diffusion mechanism. In the lower temperature range 200–550 ◦ C, activation energies for Ni–Cu diffusion vary from 41 to 131.8 kJ mol−1 [14,16,24,30]. Schwarz et al. [24] attributed such low activation energies to a grain boundary diffusion mechanism. It is therefore expected that the low activation energies obtained in the present diffusion study at low-to-intermediate temperatures reflect a dominance of grain boundary diffusion, with similar behaviour in the heat-treated Ni–Cu wires. Of the few investigations to address the compositional Table 3 Published activation energies for Ni–Cu interdiffusion.

Fig. 5. Composition-dependent Ni–Cu interdiffusion coefficients for temperatures of 400 ◦ C (), 450 ◦ C ( ), 500 ◦ C ( ), 550 ◦ C ( ) and 600 ◦ C ( ).

Temperature range (◦ C)

Activation energy (kJ mol−1 )

References

250–450 200–630 550–650 650–850 750–950 950–1050

130.5 131.8 41–221 31–53 108.8 217.6

Joubert et al. [16,29] Ruske [30] Schwarz et al. [24] Zhao et al. [14] Fisher and Rudman [13] Fisher and Rudman [13]

90

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[17] proposed that effective diffusion coefficients could be defined which depend upon both volume diffusion coefficient (Dv ) and grain boundary diffusion coefficient (Dgb ): Deff = Dv + fDgb

(5)

where f is a geometric factor which depends upon microstructure and is defined by: f =

Fig. 6. Arrhenius plot for Dc at a composition of 50 at.% Ni–50 at.% Cu.

dependence of interdiffusion in the Ni–Cu system, Ijima et al. [26] noted that below 60 at.% Ni, activation energies tend to fall with decreasing Ni concentration. In addition, Ijima et al. [26] argued that at low Ni concentrations, there would be increased quantities of voids, which would enhance interdiffusion, leading to lower activation energies. This trend is consistent with the present data. In spite of the compositional dependence of Ni–Cu interdiffusion, it is useful to adopt a mid-range composition to explore broad trends in the diffusion data. Fig. 6 therefore shows an Arrhenius plot for an alloy of the mid-range composition (50Ni–50Cu), based on the data presented in Fig. 6. 3.4. Effect of microstructure on Ni–Cu diffusion Although the present interdiffusion coefficients are consistent with literature data, there are differences between individual studies. A number of investigators explored the effect of microstructure on interdiffusion in binary metallic systems and suggested grain size has major impact on mass transport [17,18,24,31]. To assess the influence of grain size on Ni–Cu interdiffusion, relevant published data along with data from this study are presented in Fig. 7. Even within the limited dataset, the implication is that Ni–Cu interdiffusion coefficients increase with decreasing grain size. Hart

10-13 10-14

Dc (m2/s)

10-15 10-16 10-17 10-18 10-19 10-20 10-21

1.0

1.2

1.4

1.6

1.8

2.0

2.2

-1

1000/T (K ) Fig. 7. Ni–Cu interdiffusion data from: Divinski et al. [31] ( grain boundary diffusivity); Schwarz et al. [24] ( volume diffusivity and diffusivity for material with an average grain size of 10 ␮m); Zhao et al. [14] ( diffusivity for material with an average grain size of 30 ␮m); and the present work ( diffusivity for material with an average grain size of 18 ␮m).

kw d

(6)

where w is the grain boundary width (often taken to be ∼0.5 nm [32]), d is the average grain size and k is a grain shape factor, taken to be 1 for parallel grains and 3 for hexagonal shaped grains [17]. It has long been recognized that grain boundary diffusion is much faster than volume diffusion; Divinski et al. [31] demonstrated for Ni–Cu diffusion that grain boundary diffusion was several orders faster than volume diffusion at the same temperature. This is highlighted in Fig. 7. By reducing the grain size, there is an increased number of grain boundaries per unit volume, and thus at low and intermediate temperatures, grain boundary diffusion dominates the effective diffusion process, leading to enhanced effective diffusivity. Therefore, the difference between published diffusion data (such as in Fig. 7), can be understood in terms of microstructural differences. However, Kaja [18] showed that at high temperature (above 80% of the melting temperature), grain size has significantly less effect on diffusivity. It is well established that the rate of volume diffusion increases more rapidly at high temperatures than that of grain boundary diffusion because volume diffusion has a much larger activation energy. This can cause the Ni–Cu interdiffusivity to be less dependent on grain size at high temperatures. ˜ c values for microstructural effects 3.5. Correction of D It is clear that Ni–Cu interdiffusion rates depend critically on the microstructure of the constituent materials. In order to quantitatively evaluate the impact of Ni–Cu interdiffusion on the ageing of Ni coated Cu wires (in terms of changes in the effective wire resistivity) reliable and relevant diffusion data are required. Hence, the present interdiffusion data from the Ni–Cu foils needs to be corrected by the geometric factor which is relevant to the microstructure of the wires used in the resistivity investigations. The grain sizes of the polycrystalline materials used in the diffusion couples employed by Zhao et al. [14] and Schwarz et al. [24] were 30 ␮m and 10 ␮m, respectively; the average grain size of the Cu foil in the present study was 18 ␮m. The grain boundary width was assumed to be 0.5 nm for the face centre cubic-structured Cu [33]. Since the shape of the grains in the microstructure of the Cu foil was regular hexagonal, the grain shape factor (k) in Eq. (6) was assumed to be equal to 3. On this basis, the geometric factor (f) was determined for the Cu–Ni diffusivity data of Zhao et al. [14], Schwarz et al. [24] and this study using Eq. (6), and effective interdiffusion coefficients (Dc ) calculated by use of Eq. (5). As 400 ◦ C is the temperature of primary interest, the data from the literature [14,24] were extrapolated to that temperature by relevant Arrhenius relationships. Fig. 8 shows the resulting plot of effective Ni–Cu interdiffusion coefficients at 400 ◦ C as a function of the geometric factor (f). The limited dataset suggests a simple linear relationship. From Fig. 8 it is possible to obtain, by interpolation, effective interdiffusion data relevant to the Ni-coated Cu wires used in the resistivity investigations. The Cu core of the AWG20-Class3 wires had an average grain size of 7 ␮m, with grain shapes being a mixture of both hexagonal and parallel forms. The grain shape factor (k) for this wire was taken to be 2 (average of 1 and 3). In contrast, the Cu core of the AWG18-Class27 wire consisted of grains which were elongated with parallel sides, having an average grain size of 100 ␮m; this gave a grain shape factor (k) of 1. For both

Z. Wang et al. / Materials Science and Engineering B 198 (2015) 86–94

Fig. 8. Calculated effective Ni–Cu interdiffusion coefficients at 400 ◦ C as a function of geometric factor (f) based on the data of Zhao et al. [14] (), Schwarz et al. [24] ( ) and present work ( ).

wire samples the grain boundary width (w) was assumed to be 0.5 nm [33]. These data enabled the geometric factors (f) to be determined for the two types of wire (Table 4): 1.43 × 10−4 and 5 × 10−6 respectively. Interpolating the Ni–Cu interdiffusion data in Fig. 8 for these geometrical factors yielded effective interdiffusion coefficients of 1.4 × 10−17 m2 s−1 for the AWG20-Class3 wire and 5.1 × 10−19 m2 s−1 for the AWG18-Class27 wire at 400 ◦ C. A similar correction procedure can be applied to all the interdiffusion data obtained in the present work. In addition to the microstructural factors discussed above, the movement of mobile boundaries may cause further changes in the diffusion profiles under certain conditions [34]. Diffusion induced grain boundary migration (DIGM) occurs in the Ni–Cu system at low temperatures when grain boundary diffusion is most effective [34–37]. It is therefore useful to examine if DIGM would have an impact on the diffusion profiles of aged Ni-coated Cu conductors. For DIGM to operate, volume diffusion in the system needs to be ‘frozen’ out; this is denoted by the condition that volume diffusion (Dv ) divided by the velocity of grain boundary migration (v) must be less than  (a parameter approximately equal to the lattice parameter), i.e. Dv /v <  [35–37]. For the Ni–Cu system, volume diffusion data are available for a range of temperatures [13,24,38], grain boundary migration velocity data are reported by Ma et al. [37], and  ∼3.61 A˚ for Cu, enabling calculation of Dv /v. At a temperature of 400 ◦ C, Dv /v equals 4.5 A˚ for the Ni–Cu system; this value is already larger than the lattice parameter of Cu, and so fails the necessary condition for DIGM. Thus at 400 ◦ C and above, DIGM would not have a significant impact on Ni–Cu interdiffusion profiles, and it is not necessary to apply further corrections to the diffusion data. 3.6. Model for diffusion controlled ageing behaviour – lifetime With the availability of Ni–Cu interdiffusion data relevant to typical conductor wires it is possible to model the ageing behaviour of the bimetallic wires resulting from interdiffusion. Starting from the as-received Ni-coated wire, heat-treatment at elevated temperatures will cause Ni–Cu interdiffusion, and for Ni to penetrate Table 4 Microstructural data and calculated geometric factors for AWG20-Class3 and AWG18-Class27 Ni coated Cu wires. Material

d (␮m)

w (nm)

k

Geometric factor (f)

AWG20-Class3 AWG18-Class27

7 100

0.5 0.5

2 1

1.43 × 10−4 5 × 10−6

91

Fig. 9. Simulated Ni concentration-distance profiles in the AWG18-Class27 Ni coated Cu conductor aged at 400 ◦ C for 1 × 105 h (dashed line) and 1.2 × 107 h (dotted line). The solid line represents the original interface between the Ni coating and the Cu core prior to the high temperature annealing process.

progressively deeper into the Cu core. Using interdiffusion data from the foil experiments which are corrected for microstructural effects, it is possible to predict the Ni compositional profile in a Ni–Cu interdiffusion couple (equivalent to the outer region of a Nicoated Cu wire) by assuming a thick film geometry (Ni layer on top of Cu core) and use of the thick-film diffusion solution of the diffusion equation [39]: C(x,t) − C1 =

C0 − C1 √ √ 2[erf ((h + x)/2 Dt) + erf ((h − x)/2 Dt)]

(7)

where C(x,t) is the concentration at distance x from external surface of the wire after time t, D is the diffusion coefficient; C0 is the initial concentration of diffusant in the thick film (100 at.% Ni in this case); C1 is the initial diffusant concentration in the material (0 at.% Ni in this case); h is the initial thickness of the diffusant film, equivalent to the Ni coating thickness; and erf refers to the error function. Planar geometry is valid for the thick film solution as the diffusion distances are a very small fraction of the wire diameter (∼4%) giving a close approximation to linear geometry. Using Eq. (7) and corrected diffusion data for Ni–Cu interdiffusion, sets of concentration-distance profiles were calculated for Ni-coated Cu wires thermally aged at different temperatures. Fig. 9 shows simulated concentration-distance profiles in an AWG18Class27 wire, thermally aged at 400 ◦ C, for 1 × 105 and 1.2 × 107 h. It was noted that the surface concentration of the wire would reduce to less than 30 at.% Ni after a time of 1.2 × 107 h. In contrast, for the AWG20-Class3 wire, (having a much thinner Ni coating layer) it would take a much shorter time of 3200 h for the same reduction in surface concentration at the same temperature. Using the criteria of Castle and Nasserian-Riabi [40] (Ni–Cu binary alloys have good resistance to oxidation unless the alloy concentration is lower than 30 at.% Ni) these times can be regarded as the minimum at which surface oxidation will start. The growth of an oxide film on the surface of the wire will reduce the strength of the bond between the insulation and the conductor, thus degrading the insulation [40]. Therefore, the time at which the surface concentration of the wire decreases below 30 at.% Ni will help define the effective life-time of a Ni-coated Cu conductor. Using these criteria, the lifetime of a Ni-coated Cu wire was calculated as a function of coating thickness. In the case of an AWG18-Class27 wire annealed at 400 ◦ C (Fig. 10(a)), the lifetime increases with Ni coating thickness in a non-linear way; for example a wire with a coating 160 ␮m thick is predicted to have a lifetime

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Z. Wang et al. / Materials Science and Engineering B 198 (2015) 86–94

Fig. 10. (a) Calculated lifetime of a Ni-coated Cu wire as a function of Ni coating thickness for an average grain size of 100 ␮m, a grain shape factor of 1 and an annealing temperature of 400 ◦ C. (b) Calculated lifetime of a Ni-coated Cu wire as a function of grain size for a Ni coating thickness of 74 ␮m (equivalent to that of an AWG18-Class27 wire used in the wire ageing experiments), a grain shape factor of 1 and an annealing temperature of 400 ◦ C.

of 5 × 107 h (Fig. 10a). Similarly, as grain size can have a significant impact on diffusion process and thereby the ageing behaviour of the bimetallic wires, Fig. 10(b) shows the lifetime of a Ni-coated Cu wire as a function of grain size. A simple linear increase in lifetime with grain size is predicted. With an increase in grain size from 20 to 40 ␮m (and reduction in the contribution of grain boundary diffusion to Ni–Cu interdiffusion), the lifetime of the Ni-coated Cu wire would increases from 2.2 × 106 to 4.4 × 106 h.

Ni). Therefore, the effective resistivity wire of the wire of length l can be found from

A Awire i = lwire li

(9)

i

or, by canceling the wire length l at both sides of the equation,

A Awire i = wire i

(10)

i

3.7. Model for diffusion controlled ageing behaviour – effective resistivity Changes in the effective resistivity of a Ni-coated Cu wire can be simulated by adopting concentric circle geometry, where the composition of each ring is constant, and different from that of each neighbouring ring (Fig. 11). Loos and Haar [9] suggested that the effective resistance of a Ni-coated Cu conductor could be modelled by treating the pure Ni and Cu regions, and all the intermediate alloy areas as resistors in parallel. In this case, the effective resistance of a Ni coated Cu wire (Rwire ) can be found from: 1 Rwire

=

1 i

Ri

(8)

where Ri represents the resistance of a concentric circular wire of length l and alloy composition i (which varies from zero to 100 at.%

where Awire is the cross-sectional area of the wire; Ai is the crosssectional area of each alloy concentric circle, and i represents the resistivity of the corresponding alloy composition at temperature of interest. Ho et al. [11] have compiled extensive resistivity data for Ni–Cu alloys for temperatures from 300 to 700 ◦ C. In order to model the resistivity behaviour of the wires, the simulated concentration-distance profile of Fig. 9 was then sub-divided into 50 segments; for each, the alloy composition was assumed to be homogenous. Based on the sub-divisional thickness, the resulting area of each respective region in Fig. 11 could be calculated as function of thermal ageing time. The effective resistivity of the wire was then calculated (by use of Eq. (10)) as a function of ageing time using the effective interdiffusion coefficients from the foil experiments. Fig. 12 shows the calculated effective resistivity for the AWG18-Class27 wire as a function of ageing time at 400 ◦ C. The importance of employing microstructure-corrected diffusion data for calculations of resistivity and ageing effects in Ni-coated conductors is exemplified in the figure. Whilst there is an excellent agreement between the experimental resistivity data and the simulated data based on diffusion data corrected for geometrical

Fig. 11. Schematic diagram of the concentric circle geometry used for resistivity-diffusion model. The external dark rings represent regions of high Ni concentration; internal rings shown in light grey represent regions of low Ni concentration; the central white region is pure Cu.

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Fig. 12. Experimental and simulated resistivity data for AWG18-Class27 Ni-coated wire thermally aged at 400 ◦ C for 5500 h ( experimental data; dashed-dot line represents the simulated resistivity based on non-corrected diffusion data, solid line represents the simulated resistivity based on the corrected diffusion data).

Fig. 13. Simulated resistivity data for AWG18-Class27 Ni-coated Cu conductor as a function of ageing time at 400 ◦ C (solid line) and 500 ◦ C (dash-dot line);  represents the experimental data in the present study.

effects, it is clear that the original, uncorrected, Ni–Cu interdiffusion data significantly overestimates the increase in resistivity and thus the rate of ageing. This demonstrates the importance of using diffusion data which are appropriate for the samples and materials under consideration. Using the model, it was possible to predict changes in the effective resistivity of a Ni-coated Cu wire when subject to long-term high temperature annealing. Fig. 13 shows the effective resistivity of an AWG18-Class27 wire as a function of ageing time at temperatures of 400 and 500 ◦ C. As anticipated, the rate of changes in the effective resistivity of the wire, annealed at 500 ◦ C, is much faster than that of the same wire, annealed at the lower temperature of 400 ◦ C. The enhanced diffusion rate at the higher temperatures causes Ni to penetrate more quickly into the Cu core, thus forming more resistive alloying regions at the Ni–Cu interface. This leads to a higher rate of changes in the effective wire resistivity at higher temperatures. Although the initial electrical resistivity of the AWG20-Class3 wire was smaller than that of AWG18-Class27, the former exhibited a greater rate of change after 5500 h of ageing at 400 ◦ C (Fig. 1). The model also indicated that at 400 ◦ C it would take 4.8 × 104 h for a 10% increase in the resistivity of AWG20-Class3 wire, but that it

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would take 1.4 × 105 h for a similar change in the AWG18-Class27 wire, confirming the superior ageing behaviour of the AWG18Class27 Ni-coated Cu conductors. A key element in machine design involves detailed thermal modelling. The limiting design factor is the absolute temperature of the stator conductor insulation. Machine designers endeavour to predict the rated machine losses and hence temperature of the stator conductors to a high degree of accuracy, so that the design margins on temperature can be minimized and the motor volume and weight reduced. The dominant electrical losses in a machine are the winding copper losses and the iron losses in the magnetic circuit; the relative magnitudes of these vary, depending on the machine power rating. Increasing resistivity of the copper windings due to Ni–Cu interdiffusion is clearly a serious consideration for the overall machine design because the stator copper losses and temperature will increase at full rated current. This would result in a reduction of full load operating motor efficiencies but also impacts on the rating of the machine. The design process uses an estimated motor lifetime, and with knowledge of the increased copper resistance over that lifetime, the designer has two choices: either to de-rate the machine to compensate for the increased winding resistance over its lifetime (i.e. reduce the rated current); or increase the copper area of the windings to reduce the resistance leading to an increase in the motor size for the same rating (hence higher cost of manufacture). The smaller grain size of AWG20-Class3 wires appears to be responsible for more accelerated ageing. As suggested by Hart’s Equation (Eqs. (5) and (6)), a smaller grain size, and generally a larger geometric factor, leads to a much higher effective rate of interdiffusion, and thereby more accelerated ageing behaviour in terms of the wire resistivity. It is implied a Cu conductor wire having a preferred microstructure, of large and parallel grains, may exhibit superior ageing behaviour in terms of changes in the effective wire resistivity. However, the lifetime of the Ni coated Cu wire is defined as the time at which the surface concentration decreases below 30 at.% Ni; therefore, the lifetime depends critically on the thickness of the Ni coating. Although a thicker Ni coating indeed gave rise to a higher effective resistivity than a thinner Ni coating, the model predicts that lifetime of a bimetallic wire is significantly extended by thicker Ni coatings.

4. Conclusions Heat treating typical AWG20-CLASS3 and AWG18-Class27 Ni coated Cu wires at 400 ◦ C for times up to 5500 h showed that the electrical resistivity increased by 6.9% and 2.3%, respectively. Microstructural analysis revealed evidence of Ni–Cu interdiffusion, implying it was responsible for the change in resistivity. The data was consistent with known changes of resistivity of Ni–Cu alloys. Ni–Cu interdiffusion experiments at 400–600 ◦ C using metal foils enabled composition dependent interdiffusion coefficients to be determined for the system. Calculated activation energies were in the range 79–90 kJ mol−1 , consistent with a grain boundary diffusion mechanism. Detailed analysis of the available Ni–Cu interdiffusion data suggested the interdiffusion rate depends upon microstructural effects controlled by grain size, grain boundary width and grain shape, reflecting the contribution grain boundary diffusion to the effective interdiffusion rates. A concentric circle-type model was developed to simulate the changes in composition in Ni-coated conductors as a function of ageing time at elevated temperatures. The model was used to predict the life-time of the wire, which was defined as the time at which the surface concentration decreased to 30 at.% Ni and thus the surface oxidization would commence. A thicker Ni coating layer reduces the rate of Cu transport to the surface of the wire, thereby enhancing the life-time of the wires.

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