Factors Affecting the Physical Properties of Electrically Conductive Copper and Dilute Copper Alloys

Abstract

Since Cu exhibits the highest electrical conductivity among base metals and common metals, pure Cu and dilute Cu alloys are widely used as functional materials for electrical components and power transmission materials. It is also expected that in the future, conductive pure Cu and Cu alloys will continue to be used according to the desired properties by understanding inherent characteristics of pure Cu and Cu alloys. This paper reviews factors such as the contribution of lattice defects and solute elements to the electrical conductivity of pure copper, and factors affecting strengthening processes such as precipitation hardening, solid solution hardening, and work hardening in dilute Cu alloys. In precipitation hardening, the type and amount of alloying elements added and the precipitation treatment are adjusted, but softening of the Cu alloy due to overaging must be avoided. In solid solution hardening, the type and amount of alloying elements are also optimized, often in combination with work hardening. Although work hardening generally results in changes in elongation and strength after processing, the decrease in electrical conductivity due to dislocations is small. Therefore, it is effective to combine work hardening with solid solution hardening and other processes. Microstructural characterization using analytical techniques have been conducted to elucidate the electrical conductivity and strengthening mechanisms of these alloys. Their findings are useful in controlling the conductive and mechanical properties of advance Cu alloys. This review also demonstrates the usefulness of these characterization methods.

Fig. 10 0.2% proof stress of pure Cu and Cu–5Zn, Cu–5Al, Cu–5Mg, and Cu–5Sn alloys (in at%), which were as-prepared and hardened by rolling versus their electrical resistivity.³⁴⁾

1. Introduction

Cu and its alloys exhibit the highest electrical conductivity among base metals, and their fundamental properties, such as the temperature dependence of the electrical resistivity, have been investigated over a wide temperature range to understand the mechanism of their conductivity.^1–5) The electrical resistivity of Cu and its alloys is corrected for shape change owing to thermal expansion along with other noble metals. Consequently, the recommended resistivity values are published based on theoretical considerations and experimental data.²⁾ Further, the recommended resistivity values for Cu and other metals are presented together with information on the properties of the samples and measurement conditions, and explanations provided regarding the data evaluation methods result in further recommendations and other related matters. Figure 1 shows a schematic log-log plot of the relationship between electrical resistivity and temperature for different purities of Cu.⁵⁾ The temperature dependence of electrical resistivity at high temperatures is interpreted using the Bloch-Grüneisen model,^2,3) wherein the temperature dependence of electrical resistivity ρ(T) is approximately expressed as ρ ∝ T at temperatures higher than the Debye temperature (ca. 342 K at 0 K, ca. 320 K at 298 K²⁾) and ρ ∝ T⁵ at lower temperatures.⁶⁾ The effects of impurity elements and lattice or crystal defects on the electrical resistivity of Cu have also been studied, wherein scattering by impurity elements and lattice phonons during electron transfer has been discussed. The resistivity of an impure metal is generally given at any temperature, T, by the following relationship.   

\begin{equation} \rho_{\text{tot}} = \rho_{\text{ph}} + \rho_{\text{o}}, \end{equation} (1)

where ρ_tot is the resistivity of the impure metal at temperature T, ρ_ph (“ph” denotes phonons) is the resistivity that a pure, perfect crystal of the metal would have at this temperature, and ρ_o is the resistivity that the impure metal has at very low temperatures.

Fig. 1

Electrical resistivity of copper of different purities at low temperatures.⁵⁾

The contribution of impurity elements to the electrical resistivity of Cu appears to be significant in the low-temperature region, as shown in Fig. 1. The contribution of each impurity element to the electrical resistivity is approximately additive, which is referred to as the Matthiessen’s rule. Other terms for lattice defects are also added when electrical resistivity increases with lattice defects owing to plastic deformation.⁷⁾ However, deviations from Matthiessen’s rule are often observed, depending on the sample conditions. For example, Matthiessen’s rule deviated from experimental values when measuring the electrical resistivity of dilute Cu alloys with trace additions of Au, Ni, Ge, etc.⁸⁾ In the study on the electrical resistivity,⁸⁾ the concentration of each alloying element and residual resistivity, which is measured at sufficiently low temperatures or at 4.2 K, were determined, and the contribution of elements to the resistivity (Ωm/at%) of impurities was expressed with sufficient accuracy. Although crystal defects may be considered as impurities, scattering processes of electrons by dislocation and interfaces seem to be different from those of point defects and solute impurities.

The electrical resistivity of the industrial standard for Cu is determined as 1.7241 × 10⁻⁸ Ωm at 293 K, which is the electrical resistivity of the International Annealed Cu Standard (IACS). The percentage of electrical conductivity corresponding to the resistivity is referred to as %IACS.⁹⁾ When the %IACS of the standard Cu is considered as 100%, the electrical conductivity of oxygen-free Cu (OFC) or oxygen-free high conductivity Cu (OFHC) is slightly higher than that of the IACS, exceeding 100%. Cu and its alloys exhibit high electrical conductivity and good formability. Consequently, they are used in a wide range of industrial fields ranging from small electrical components to power transmission and other fields.^10–12) For example, advances in automotive electronics technology have resulted in the development of high-performance electronic and electrical devices, which require connectors and other components to be smaller, thinner, more multifunctional, and lighter. In particular, to transmit electrical signals reliably even in high-temperature environments, connectors are required to possess heat resistance to suppress the stress relaxation phenomenon caused by heat generation owing to the high current density.

Furthermore, Cu and its alloys have attracted attention as conductive materials in the internal wiring of semiconductor packages, lead frames used in connectors for electrical connections, and ultra-thin films less than ca. 0.1 µm in thickness for integrated circuits (e.g., Ultra Large-Scale Integration).¹³⁾ To understand the size effect on the conductivity of pure Cu, the size effects on the residual resistivity of wires were investigated using pure Cu and several dilute Cu alloys. The size effects were shown to significantly affect the conductivity of pure Cu, although previous studies have not fully considered them. Bonding wires utilizing Cu have also been developed as an alternative to bonding wires using Au.^14–16) The properties of surface-coated, uncoated, and bare Cu bonding wires have been compared. The quality of the core wire in surface-coated wire with a thin coating of Pd or Au–Pd alloy was the same as that of the uncoated wire. The bonding wire diameter was ca. 25 µm, and the electrical resistivity was approximately 1.9 × 10⁻⁸ Ωm. It is expected that the bond reliability of Cu bonding wires will be increased by improving the surface coating.

Thus, numerous studies have been performed on the physical properties of Cu and its alloys against the extensive background, wherein the use of Cu and it alloys was discussed. However, focusing on the electrical resistivity or conductivity of pure Cu for application to small or smart devices and considering the improvements to the mechanical strength of Cu at approximately room temperature is more beneficial. Moreover, reliable information obtained from various analytical methods must be reviewed to understand the effects of microstructural modification of Cu via the addition of alloying elements. In recent years, the understanding of the relationship between properties and microstructures has increased owing to the development of quantum-beam analysis methods. Thus, this paper reviews a number of studies on the physical properties, such as the electrical and mechanical properties, of pure Cu and dilute Cu alloys containing less than approximately 5% elements, while focusing on the effects of size and solute elements on electrical conductivity or electrical resistivity (Chapter 2). In addition, particular emphasis was placed on the role of lattice defects (point defects, dislocations and interfaces) on the physical properties (Chapter 3), and the effects of dissolution and precipitation of alloying elements on the physical properties (Chapter 4) by investigated using methods of structural analysis.

2. Electrical Resistivity of Cu and Dilute Cu Alloys

2.1 Effect of size on electrical resistivity of pure Cu

Cu and its alloys are generally more conductive than other base metals, such as aluminum and iron. Typical Cu is widely used as an electrical material is electrolytic tough pitch Cu (ETP-Cu: 99.90% or higher), which contains a small amount of oxygen, and oxygen-free Cu (OFC: 99.96% or higher), wherein oxygen and impurities are in reduced form. Such pure Cu exhibit good electrical conductivity and are used for power transmission cables, small lead frames, and connectors. Since pure Cu and its dilute alloys are also used in small dimensions, it is important to consider the size effect on the resistivity.

To improve the mechanical strength along with the electrical conductivity, the size of wiring and crystalline defects such as internal twins and grain boundaries are important factors.^17–25) For example, the size effects on the resistivity were investigated for wires with different ratios of diameter/electron mean free path at low temperatures. Consequently, the size effects were shown to significantly affect the conductivity of pure Cu, although previous studies have not fully considered them.¹⁸⁾ Furthermore, related to the size effect, a study was conducted to evaluate several purities of Cu with high precision in terms of the residual resistivity ratio (RRR: ratio of electrical resistivity at approximately room temperature and liquid helium temperature of 4.2 K.²¹⁾ High purity Cu (5N and 6N grades) with diameters in the range of 0.2–2 mm were used as samples, and these wires were heat treated under appropriate conditions to investigate the dependence of RRR on heat treatment conditions and diameter (size effect) before RRR measurement. Consequently, the optimum annealing temperature and time were determined to be 923 K and 14.4 ks (4 h) or greater, respectively. The relationship between the size effect of RRR, RRR_W (RRR measured on Cu wire with diameter d), RRR_B (RRR of bulk Cu), and diameter d (mm) was determined as follows:   

\begin{equation} RRR_{\text{W}}{}^{-1} = RRR_{\text{B}}{}^{-1} + (3.8 \times 10^{-5})\cdot d^{-1} \end{equation} (2)

When RRR_B is very large and RRR_B⁻¹ is zero for high-purity Cu, this plot resembles the broken line shown in Fig. 2. The slope of this plot was used to obtain the product of the electrical resistivity ρ of pure Cu at 4.2 K and the mean free path λ of electrons, ρ − λ, as 6.5 × 10⁻¹⁶ Ωm². As the electrical resistivity of high-purity Cu at 298 K is 1.69 × 10⁻⁸ Ωm, the product value is reasonable. Moreover, it was also shown that the difference in RRR_W of Cu wires of different purities is dependent on the sample diameter, which increased as the purity of the sample increased.

Fig. 2

Effect of wire diameter on RRR value of copper of different purities.²¹⁾

In addition, to understand the effect of the line width on the resistivity of Cu at low temperatures, the resistivity of submicron Cu wires with line widths in the range of 75–500 nm was measured at temperatures of 10–380 K.²²⁾ From these results, it was estimated that for the thinnest line with a line width of 75 nm, the electron scattering contribution at 20 K was 29% from the Cu surface, 25% from grain boundaries, and 30% from impurities. The remaining 16% was attributed to the bulk resistivity. It was also suggested that the electron-phonon scattering contribution is approximately 60% at 300 K. It is worthwhile to recognize different scattering mechanisms at different temperatures.²²⁾

Since the size of twins and crystalline grains influences the electrical resistivity, the size effects of twins and grains on the electrical resistivity of pure Cu have also been investigated.^23–29) For example, pure ultrafine Cu particles were synthesized through pulse electrodeposition.^23,24) The twin density was varied by adjusting the processing parameters. The electrical resistivity of the Cu samples with 15 nm twin spacing at room temperature was 1.75 × 10⁻⁸ Ωm (conductivity was approximately 97% IACS), which was comparable to that of pure Cu samples with coarse crystal grains. When the twin density was reduced for the same grain size (twin lamella spacings decreased from 90 nm to 35 nm), the electrical resistivity increased from 1.75 to 2.12 × 10⁻⁸ Ωm.²³⁾

To clarify the effect of the film thickness on the electrical resistivity of Cu, it is desirable to characterize the sheet resistance, film thickness, and average grain size of thin Cu films.^26–29) For example, through resistivity measurements, profilometry, electron backscatter diffraction, and X-ray diffraction, the properties of thin films (approximately 10–150 nm thick) were measured.²⁶⁾ These results showed that the electrical resistivity of the films increased with decreasing film thickness. Further, they were compared to the calculated values using the measured average grain size and fitting parameters for surface and grain boundary scattering. The experimental values were consistent with the thickness dependence of the resistivity obtained using a general-purpose simulation program.

2.2 Contribution of solute elements to electrical resistivity of Cu

In pure Cu, a small amount of alloying elements is added to increase the mechanical strength. However, the addition of alloying elements generally induces a decrease in electrical conductivity or an increase in electrical resistivity. Thus, alloying elements are carefully added while considering the decrease in the electrical conductivity. Because solute elements in Cu increase electrical resistivity and strength, their contribution to electrical resistivity has been investigated in detail using high-purity Cu.^30,31) Figure 3 demonstrates the increase in electrical resistivity at 298 K when a small amount of different alloying elements was added to Cu.³¹⁾ If the resistivity is compared for a given amount of alloying elements in mass%, the electrical resistivity was found to increase in the order of Zn < Ag < Ni < Sn < Al < Mn < Cr < Si < Co. Although Mg does not appear in this figure, its contribution to the resistivity appears to be comparable to that of Ag as per recent studies.^32–34)

Fig. 3

Effect of alloying elements on the resistivity of copper.³¹⁾

When the amount of alloying elements in Cu increases, a precipitate or second phase may form in the matrix. Then, the amount of alloying elements dissolve in Cu and the electrical resistivity are likely to nearly unchanged, although the size of the precipitate influences the solubility. Precipitation in multicomponent systems, such as a Cu–Ni–Si system, further reduce the amount of dissolved or solute elements if the precipitates are composed of different alloying elements, as discussed in precipitation hardening. Pure Cu contains residual oxygen family elements (chalcogens), such as sulfur and tellurium, which primarily originate from the electrolytic bath during electrolytic refining.⁵⁾ As the amount of these non-metallic elements increases, non-metallic inclusions may easily form owing to low solubility. Such non-metallic inclusions may induce a yield loss of Cu during processing. In addition, non-metallic inclusions are undesirable because they degrade the surface properties and formability. Thus, purification of the starting Cu is important for achieving a high conductivity of the final products.

3. Lattice Defects in Cu and Cu Alloys

3.1 Point defects in pure Cu

The characteristics of point defects in pure Cu were investigated by introducing defects using quenching from high temperatures and particle irradiation or deformation at low temperatures.^35–40) To investigate the recovery processes of point defects in Cu following irradiation with charged particle beams, the electrical resistivity of Cu was measured at low temperatures. In this study on the recovery processes of point defects, the Cu point defect recovery model and modified models were discussed.³⁵⁾ It was considered that two types of interstitial structures: crowdions and normal self-interstitials, are generated by electron irradiation. Further, the crowdions and normal self-interstitials revealed a recovery stage at low temperatures. Crowdions were then formed in the vicinity of the normal self-interstitials and dislocations, and vacancy complexes were relatively stable at room temperature.³⁵⁾ The formation and recovery of point defects in Cu was also investigated by irradiation of neutrons and electrical resistivity measurements at 4.2 K.³⁹⁾ The results showed that the damage production and annihilation rates obtained in experiments were consistent with the predictions based on damage energy calculations, and point defects were annealed out through annealing up to approximately room temperature.³⁸⁾ Since the electrical resistivity due to point defects is almost recovered to room temperature, it was generally shown that contribution of point defects to the electrical resistivity is very small near room temperature.

3.2 Interfaces in pure Cu and Cu alloys

To investigate the contribution of grain boundaries (GBs) to the electrical resistivity of Cu, single-crystal wires fabricated via crystal growth were used to measure the electrical resistivity of Cu.^24,25) A process was developed to grow Cu single crystals using the Czochralski method to produce wires. The electrical resistivity of single crystals showed a 9% reduction compared to the IACS electrical resistivity, indicating that GB significantly affected the resistivity above 70 K.²⁴⁾ To understand the effect of the GB structure on the resistivity of Cu, the resistivity of Cu with different GB structures was measured. Although it is difficult to compare the electrical resistivity of GBs with other defects, the electrical resistivity was shown to be strongly dependent on the structure of the GBs. It was concluded that the electrical resistivity of the GB was approximately correlated with the excess volume of the GB.²⁵⁾

Interfaces such as grain and twin boundaries also play an important role in the mechanical strength of Cu and Cu alloys because they increase with decreasing grain size.⁴¹⁾ For example, it was shown that pure Cu samples with dense nanoscale twins exhibit approximately 10 times the tensile strength of coarse-grained Cu, with less conductivity loss.⁴²⁾ It is considered that general fine grains with boundaries formed in Cu and Cu alloys also influence their mechanical strength. These samples were prepared from an electrolyte containing CuSO₄ using pulse electrodeposition. Similarly, it was shown that submicrometer-sized grains are synthesized via pulsed electrodeposition, and that they exhibit high strength owing to fine twins formed by electrodeposition.^43,44) Furthermore, it has been shown that high strength can be obtained by the introduction of twins into Cu through strong processing such as cold rolling.⁴⁵⁾

3.3 Dislocations in pure Cu and Cu alloys

It is considered that dislocations introduced into Cu do not significantly contribute to the electrical resistivity of Cu; however, they are considered to affect the mechanical strength of Cu. This has been established to evaluate the dislocation density and characteristics of metals such as Cu using X-ray or neutron diffraction.^46–59) In these studies, single crystalline and polycrystalline Cu were used, and dislocations were introduced via the use of large or cyclic deformation and particle irradiation. A recent method for estimating dislocation density involved fitting the entire powder diffraction pattern to be measured with the sum of a polynomial background and a theoretical profile function. This method is referred to as line profile analysis, specifically the convolutional multiple whole profile (CMWP) fitting method.⁵⁸⁾ The procedure provides the characteristic parameters of the crystallite size distribution function and dislocation structure. In the CMWP method, a theoretical line profile is obtained by performing convolution integration (crystallinity-derived and device-derived line profiles) and fitting it to the measured line profile. The crystallinity-derived line profile is the convolution integral of the line profile owing to crystallite size effects and the line profile owing to the micro-strain generated by dislocations.

The dislocation density of the entire sample was estimated by fitting a theoretical curve to the experimental values. Figure 4 shows the CMWP fitting for the X-ray diffraction pattern of the cold-rolled Cu–2Mg (in at%) specimen at an equivalent strain of 0.30.⁶⁰⁾ This method can detect dislocation densities over approximately 1 × 10¹³ m⁻² and is useful for studying the relative variations in dislocation density caused during plastic deformation.

Fig. 4

CMWP fitting for the X-ray diffraction pattern of the cold-rolled Cu–2 at%Mg specimen at an equivalent strain of 0.30.⁶¹⁾

Figures 5(a) and (b) show the variations in the total dislocation density of Cu–2Sn and Cu–2Mg alloys (in at%), respectively, as a function of the equivalent strain at room temerature.⁶⁰⁾ The alloys were plastically deformed through tensile tests or cold rolling. The results indicate that the total dislocation densities increased with increasing strain and were dependent on the deformation mode. The difference in dislocation density between the tensile deformation and cold rolling is larger for Cu–2Sn than for Cu–2Mg. This indicates that tin and magnesium dissolved in Cu interact with dislocations in different ways. Since the stacking fault energy of Cu–Sn alloys is lower than that of Cu–Mg alloys, deformation twins form more frequently in Cu–Sn alloys.⁶⁰⁾ Thus, some differences in the dislocation densities in the deformation mode may be caused by the inhomogeneity of plastic deformation in the alloys.

Fig. 5

Total dislocation densities of (a) Cu–2 at%Sn, and (b) Cu–2 at%Mg alloys as a function of the equivalent strain.⁶¹⁾

3.4 Dislocation dynamics from low temperature to high temperature

Point defects in Cu are mobile at low temperatures and are almost completely annealed out at room temperature. However, dislocations in Cu are mobile in a very short range at temperatures below room temperature and can be rearranged at high temperatures. The dislocation motion in a short range at low temperatures is observed as internal friction peaks in a pure Cu.^62–77) This is referred to as dislocation relaxation, which has been investigated using deformed pure Cu by many studies. Internal friction experiments were conducted under various conditions. For example, the internal friction of several cold-worked Cu single crystals was measured below room temperature at a frequency of kHz under vibrational strain amplitudes in the range of 10⁻⁷ − 2 × 10⁻⁵.⁶⁹⁾ The results showed that the height of the relaxation peak increased slightly with strain amplitude for pure Cu samples; however, the activation energy of the relaxation process was unaffected by the samples. Figure 6 shows the internal friction profiles of deformed polycrystalline Cu versus temperature, which were measured at different amplitudes under approximately kHz.⁷¹⁾ It is shown that an internal friction peak is observed in both single and polycrystalline Cu, and this peak is not observed in well-annealed Cu.^67,71) Thus, the results indicate that dislocations introduced in Cu by deformation at low temperatures are mobile in the short range, even below room temperature. Further, the height of the internal friction is influenced by the relaxation process of dislocation motion.

Fig. 6

Schematics of internal frictions of deformed polycrystalline Cu versus temperature measured under different amplitudes.^69,71)

However, dislocations in Cu can be fully rearranged at high temperatures and induced during deformation at high temperature.^79–81) The dislocation dynamics or dynamic recrystallization of Cu depends on the deformation temperature. Figure 7 shows the true stress-strain curves for pure Cu at 298, 573, 673, and 773 K.⁸¹⁾ The flow stress level during deformation decreases from near room temperature up to approximately 673 K. However, the macroscopic flow stress level appears to fluctuate during deformation at 773 K.

Fig. 7

True stress-strain curves of pure copper deformed at 298, 573, 673 and 773 K.⁸¹⁾

To investigate the dislocation density in Cu during deformation at high temperature, neutron diffraction was used to evaluate the dislocation density in situ, as shown in Fig. 8.⁸¹⁾ The dislocation density increased monotonically with increasing strain during deformation at 573 and 673 K, whereas the dislocation density varied during deformation at 773 K. This corresponds to the changes in the flow stresses shown in Fig. 7, indicating that the dislocation density affects the macroscopic deformation characteristics.⁸¹⁾

Fig. 8

Change in dislocation density with true strain at (a) 573, 673, and (b) 673 K.⁸¹⁾

OFHC and ETP-Cu with different grain sizes were deformed at different true strain rates in the temperature range of 725–1075 K to investigate the effect of the initial grain size on the dynamic recrystallization of Cu.⁷⁸⁾ In this study, the density of twins and the density of deformation bands were measured with strain rates and stresses, although the measurements were not in situ. The density of twins decreased with increasing initial grain size, and the density of deformation bands increased with increasing initial grain size.

4. Factors Affecting Mechanical Properties of Cu Alloys

The mechanical strength of Cu and Cu alloys is generally known to increase with decreasing grain size, and the relationship between the strength and grain size (Hall-Petch relationship) is dependent on the type and composition of the alloying element.⁴¹⁾ To evaluate the grain size, the electron backscatter diffraction (EBSD) method has been employed. For example, Fig. 9 shows inverse pole figure (IPF) maps of Cu–30 mass%Zn alloys with grain sizes of 5, 20, and 60 µm, which were obtained by the EBSD method.⁶⁰⁾ The EBSD method is used to characterize the microstructure, such as texture and dislocations, as well as grain size by plastic deformation.^82–85) The microstructure of high-strength Cu composed of fine twins was also characterized by EBSD.^23,25) As the mechanical strength of Cu and Cu alloys is influenced by the dissolution and precipitation of alloying elements, types of dislocations, and anisotropy or texture, and residual stresses of Cu and Cu alloys are discussed in this chapter.

Fig. 9

IPF maps of Cu–30 mass%Zn alloys with grain size of (a) 5 µm, (b) 20 µm and (c) 60 µm.⁶⁰⁾

4.1 Dissolution and precipitation of alloying elements

The alloying elements added to Cu alloys affect their physical properties, depending on the state of the alloying elements in the Cu alloys. In solid-solution-hardened Cu alloys, work hardening by deformation is dependent on the type of the alloying element. Figure 10 shows the 0.2% proof stress of pure Cu and Cu–5Zn, Cu–5Al, Cu–5Mg, and Cu–5Sn (in at%) alloys, which were as-recrystallized and hardened by different equivalent strains via rolling versus their electrical resistivity.³⁴⁾ The contribution of alloying elements to the electrical resistivity (10⁻⁸ Ωm/at%) increased in the order Zn < Mg < Al < Sn, and they slightly increased with strain. These results are comparable to those given in Fig. 3, where the concentrations are plotted as mass%. Work hardening by the addition of Mg to Cu appears to be the largest among the elements with low contribution to resistivity. The characteristics of work hardening by Mg addition were explained by the solubility and volume-size factor of Mg in Cu alloys.^86–88) The characteristics may be related to changes in the total dislocation densities of Cu alloys by strain, as shown in Fig. 5. Stacking faults in Cu alloys may also affect work hardening, although details are unclear.

Fig. 10

0.2% proof stress of pure Cu and Cu–5Zn, Cu–5Al, Cu–5Mg, and Cu–5Sn alloys (in at%), which were as-prepared and hardened by rolling versus their electrical resistivity.³⁴⁾

Cu–Ni–Si alloys, typically Cu–2.6Ni–1.3Si (at%),⁸⁹⁾ are known to be strengthened by the precipitation of nickel and silicon by adequate aging, after these elements are supersaturated in Cu by quenching from a high temperature (solution treatment). Then, the electrical resistivity decreases because dissolved nickel and silicon are precipitated as δ-Ni₂Si during aging.^89–96) However, if the alloys are excessively aged, the strength of the precipitation-hardened alloy decreases. This phenomenon is referred to as overaging, which is caused by the coarsening of precipitates, indicating that aging conditions should be carefully selected. Interestingly, the addition of a small amount of Fe into Cu–Ni–Si alloys can delay overaging by long-term aging.⁹⁵⁾ To investigate the effect of Fe on precipitation, Cu–2.6Ni–1.3Si (at%) alloy and Cu–2.5Ni–1.3Si–0.3Fe (at%) alloys were prepared and isothermally aged at 720 K after solution treatment. Figure 11 shows the Vickers microhardness as a function of aging time. The hardness of the Cu–Ni–Si alloy increased with aging up to 5 ks, was maintained up to 10 ks, and softened when over 20 ks. In contrast, the Cu–Ni–Si–Fe alloy did not soften until 50 ks, suggesting that over-aging was significantly delayed by Fe. This result implies that a small amount of Fe may act as a stabilizer for δ-Ni₂Si precipitates.

Fig. 11

Vickers hardness of Cu–Ni–Si and Cu–Ni–Si–Fe alloys as a function of aging time at 720 K.⁹⁵⁾

To understand the effect of Fe on precipitation, the local structures around Ni and Fe were investigated using the extended X-ray absorption fine structure (EXAFS) method, which provides information on the local structure of a specific element in Cu alloys.⁹⁵⁾ The Ni–K and Fe–K EXAFS functions of the Cu–Ni–Si–Fe samples annealed at 720 K for 0, 10, 20, 50, and 200 ks, and references of metallic Fe were measured. The results show that the shape of the Fe–K EXAFS spectrum changed with aging and was analogous to that of the Ni–K EXAFS spectrum of the alloy aged up to 20 ks.⁹⁵⁾ To compare the local structure of Fe in the Cu–Ni–Si–Fe alloy after aging at 720 K for 0, 10, 20, and 50 ks, and references of metallic Cu and Fe, the radial structure function (RSF) was obtained from the Fourier transform of the Fe–K EXAFS spectra of each alloy. Figure 12 shows the RSF from the Fe–K EXAFS spectra of the Cu–Ni–Si–Fe alloy aged for 0, 20, and 50 ks. The RSFs of the reference materials, Cu and Fe, are shown. The RSF of the alloy aged for 0 s indicates atom pairs (broken arrows) characteristic of the FCC structure. These correlations disappeared in the RSF of the alloy aged for 20 ks, which may be owing to the formation of (Ni_2−xFe_x)Si. Whereas, in the RSF of the alloy aged for 50 ks, the correlations at 0.35 and 0.45 nm (solid arrows), which are characteristic of BCC-Fe, were observed. This indicates that Fe in (Ni_2−xFe_x)Si changes to precipitate as BCC-Fe during aging for 50 ks. Thus, the decomposition of microscopic precipitates is likely to be suppressed by the formation of (Ni_2−xFe_x)Si owing to its thermal stability.⁹⁵⁾

Fig. 12

Radial structure function of Fe of Cu–Ni–Si–Fe sample annealed at 720 K for 0, 20, and 50 ks, and references of metallic Cu and Fe.⁹⁵⁾

Thus, X-ray absorption spectroscopy provides useful structural information with high statistical accuracy related to the properties of Cu alloys. Furthermore, transmission electron microscopy (TEM), small-angle X-ray or neutron scattering (SAXS or SANS), and atom probes (AP) are potential methods for characterizing the size of precipitates in Cu alloys because nanometer-sized particles play an important role in strengthening Cu alloys.^97,98)

It is also known that the physical properties of supersaturated Cu–Ti alloys change during aging.^99–104) Cu₄Ti precipitates are formed from the Cu–Ti alloy during aging, which decreases and increases the electrical resistivity and strength, respectively. In this system, spinodal decomposition may occur in the matrix as a preliminary step of precipitation, resulting in periodic fluctuations in Ti concentration. After decomposition, Cu₄Ti is precipitated in the Ti-enriched region.¹⁰⁴⁾ The period of Ti concentration modulation was evaluated by analyzing the sideband peak changes in X-ray diffraction to determine the frequency of precipitate formation.

4.2 Distribution and densities of dislocations

In the work hardening of metals and alloys, flow stress and stored energy are often discussed in terms of the distribution and densities of dislocations.¹⁰⁵⁾ Two different characteristics of dislocations in metals are of interest: statistically stored (SS) and geometrically necessary (GN) dislocations. This is because they may play a different role in plastic deformation. GN dislocations are necessary to change the shape of gains in metals and alloys, whereas SS dislocations are dislocations with zero net Burgers vectors, such as tangle and dipole dislocations. The density of SS dislocations can be estimated from the difference between the total dislocation density obtained by the CMWP method and the density of GN dislocations. The density of GN dislocations is estimated from the kernel average misorientation (KAM) map of EBSD.^106,107) In the analysis, the grain was divided into hexagonal pixels, and the average of the orientation difference between the reference pixel and the surrounding pixel points was the local KAM value. Further, local orientation differences within EBSD observations are calculated as KAM values, and the GN dislocation density can be calculated from these KAM values.¹⁰⁶⁾ The value averaged over the entire observation area is the average KAM value.

Two characteristics of dislocations, GN and SS, are important in stress relaxation, as they are phenomena based on dislocation motion, which is introduced by plastic deformation. In general, stress relaxation tends to occur when the dislocation density is high. To improve stress relaxation resistance, it is effective to anneal deformed alloys at temperatures above room temperature and below 773 K after cold rolling.¹⁰⁸⁾ Annealing may reduce the dislocation density; however, it improves the stress relaxation resistance through the interaction between dislocations and solutes. To understand the mechanism of this change in the stress relaxation properties owing to annealing, the changes in the GN and SS dislocation density owing to annealing were investigated. Here, the GN and SS dislocation densities of solid-solution Cu–2 at% X (X = Mg, Sn) alloys were calculated in relation to the stress relaxation properties of Cu–Mg and Cu–Sn alloys annealed at different low-temperature annealing temperatures. Figure 13 shows the change in the stress relaxation rate of these alloys with increasing annealing temperature. For the stress relaxation test, the plate specimens were cantilevered in bending displacement and held at 453 K for 24 h. Subsequently, the displacement was measured when the specimens were unloaded.¹⁰⁸⁾ For both alloys, the stress relaxation rate decreased with increasing annealing temperature, whereas the stress relaxation resistance increased. Comparisons of the Cu–Mg and Cu–Sn alloys revealed that Cu–Mg alloy exhibited better stress relaxation resistance. This may be due to differences in the interactions between the dislocations and solute elements.

Fig. 13

Stress relaxation fraction of Cu–2 at% Mg and Cu–2 at% Sn alloys as a function of annealing temperature.¹⁰⁸⁾

Figure 14 shows the change in the total dislocation density determined by X-ray diffraction and the GN dislocation density determined by EBSD with annealing at various temperatures. The difference between the total and GN dislocation densities corresponds to the SS dislocation density. The GN dislocation density undergoes minimal change with increasing annealing temperature; however, the SS dislocation density decreases. This indicates that the SS dislocations are mainly rearranged by annealing. The total and GN dislocation densities of the Cu–Sn alloys tended to be higher than those of the Cu–Mg alloys. The small difference in the GN dislocation density between the Cu and Mg and Cu–Sn alloys suggests that the superiority of the stress relaxation resistance properties of each Cu–Mg alloy is primarily because of the lower SS dislocation density. The difference in the stress relaxation properties of the respective Cu–Mg alloys is small.¹⁰⁸⁾ The above-mentioned relationship between flow stresses and dislocation densities was also investigated in ferritic and austenitic steels, and it was validated that the method is useful for discussing the work hardening of alloys.^109–111)

Fig. 14

Total dislocation density and GN dislocation density of Cu–2 at% Mg and Cu–2 at% Sn alloys as a function of annealing temperature.¹⁰⁸⁾

When Cu alloys are applied to connectors, stress relaxation is an important property, in addition to conductivity. Stress relaxation is the time variation under an elastic stress obtained by constant strain.^112–116) This may be caused by a creep phenomenon owing to a dislocation motion over a relatively short distance. The kinetic equation of stress relaxation can describe the stress relaxation properties, and has been proposed to predict the stress relaxation of alloys under different processing conditions.¹¹⁶⁾

4.3 Anisotropy of the microstructure and elasticity

In the practical use of Cu and its alloys, the anisotropy of the microstructure of polycrystalline grains influences the mechanical properties.^117–120) The typical anisotropy of the microstructure is found as the texture of polycrystalline Cu and its alloys is texture.^117–120) Figure 15 shows the {111}, {200}, and {220} pole figures of the dilute Cu alloy (2.6Ni–1.3Si, in at%). Such a texture is observed in other Cu or dilute Cu alloys, which were investigated using different approaches in previous studies.^117–120)

Fig. 15

(a) {111}, (b) {200}, and (c) {220} pole figures of a dilute Cu alloy sheet.

The orientation preference for the rolling direction (RD) of a rolled dilute Cu alloy (2.6Ni–1.3Si, in at%) is expressed as the inverse pole figure of the RD, as shown in Fig. 16(a). Texture formation is related to the large crystallographic orientation dependence of the elastic modulus of Cu. Figure 16(b) shows the orientation dependence of Young’s modulus of Cu, wherein the Young’s modulus of Cu is small in the ⟨100⟩ orientation and large in the ⟨111⟩ orientation.¹²¹⁾ The orientation dependence of Young’s modulus of Cu corresponds to the inverse pole figure, which implies that grains with an elastically hard ⟨111⟩ orientation tend to orient in the rolling direction.

Fig. 16

(a) Inverse pole figure of RD of a dilute Cu alloy sheet and (b) 3D description of anisotropic Young’s modulus of Cu.¹²¹⁾

The texture and elastic anisotropy of Cu also appear to be related to the residual stresses in the Cu and dilute Cu alloy sheets. This is because residual stresses are considered as self-equilibrating internal stresses in free bodies that have no external forces or constraints acting on their boundaries.¹²²⁾ It is known the internal stresses in metals and alloys are changed by the microstructure or texture formed during proccessings.^48,49) It is therefore interesting to compare the residual stresses measured in dilute copper alloys with the texture, i.e., the anisotropy of the mechanical properties of the sheet.

Figure 17 shows the principal residual stresses in the dilute Cu alloy (2.6 Ni–1.3Si, in at%) as-rolled and the Cu alloy annealed at 623 K. The residual stresses in different directions of the alloy sheets were measured using the X-ray diffraction method. The results show that a large compressive stress remained in the RD, and this stress state decreased; however, it remained after annealing. Because certain arrangement of dislocations can occur in Cu annealed in dilute Cu alloys at 623 K, this arrangement may reduce the residual stresses. The residual stresses also provide information on the mechanical properties, although the measuring volume and inhomogeneity of internal stresses should be considered when evaluating residual stresses.^123,124)

Fig. 17

Compressive principal stresses with respect to RD (y-axis) and TD (x-axis) in (a) a rolled dilute Cu alloy sheet (left) and (b) an annealed alloy sheet (right).

5. Conclusion

This paper reviews the metallurgical factors that affect the physical properties, such as electrical and mechanical properties, of pure Cu and dilute Cu alloys, based on the results obtained in previous systematic investigations. It is not easy to organize these factors because they include complex effects on the physical properties depending on the types of alloying elements and dislocations. To obtain reliable information on the factors affecting the physical properties of dilute alloys, well-defined samples of high-purity Cu with carefully added alloying elements must be prepared, and accurate experiments must be performed on them. The results of those experiments can reveal the contribution to electrical resistivity and strength of dilute Cu alloys with small additions of certain elements. In discussing them, the inherent behavior of elements and lattice defects in pure copper and Cu alloys must be taken into account, although they are not necessarily well understood. Nevertheless, there appears to be a trade-off between electrical conductivity and mechanical strength.^125–128) Therefore, it is desirable to clarify the effects of trace elements in refined copper and copper alloys with few impurities other than the elements of interest.¹²⁹⁾ Furthermore, in the future, there are also issues related to the low grade of copper ores and the environment of by-products, and interdisciplinary approaches to new problems are required, taking these issues into consideration.

Acknowledgments

This study was supported in part by a grant from the Japan Cu Association and Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science. The authors would also like to express their sincere thanks to Professor M. Isshiki, Associate Professor K. Mimura, and Associate Professor Y. Onuki for their helpful discussions. S.S. would like to express his gratitude to the late Professor A. Seeger, the late Dr. M. Wilkens, Professor H. Mughrabi, Professor T. Ungàr, and Dr. G. Ribárik for their discussions on lattice defects. Part of this article was presented by one of the authors (S.S.) at a plenary lecture at the Spring Meeting of the Japan Institute of Metals and Materials (JIM) held in 2023. He also appreciates the appointment of a fellow by JIM for human resource development. The supports for measurements and analysis of texture and residual stresses by Professor S.-I. Tanaka, Professor M. Kumagai, Mr. T. Tanno and M. Chiba are appreciated.

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