Kinetics of Solid-State Reactive Diffusion in the Cu/Zn System
2017 Volume 58 Issue 1 Pages 16-22
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2017 Volume 58 Issue 1 Pages 16-22
The kinetics of the solid-state reactive diffusion between pure Cu and Zn was experimentally examined using sandwich Zn/Cu/Zn diffusion couples prepared by a diffusion bonding technique. The diffusion couples were isothermally annealed in the temperature range of 523–623 K for various times up to 49 h. Owing to annealing, an intermetallic layer consisting of the γ and ε phases was formed at the original interface in the diffusion couple, where the thickness is much smaller for the ε phase than for the γ phase. The total thickness of the intermetallic layer increases in proportion to a power function of the annealing time. The exponent of the power function takes values of 0.60–0.62 at 523–623 K. These values of the exponent indicate that volume diffusion predominantly controls the layer growth and interface reaction partially contributes to the rate-controlling process.
In the binary Sn–Zn system, the eutectic reaction L → Sn + Zn occurs at a temperature of Te = 472 K.1) Here, the concentration of Zn in the liquid (L) phase is 15 at% (9 mass%), the solubility of Zn in the Sn phase is smaller than 1 at%, and that of Sn in the Zn phase is negligible. Since the eutectic temperature Te is much lower than the melting temperature of pure Sn with Tm = 505 K, the eutectic Sn–Zn alloy is used as a Pb-free Sn-base solder with low-melting temperature in the electronics industry.2–8) On the other hand, Cu-base alloys are widely utilized as conductor materials owing to high electrical conductivity. If the Cu-base conductor is interconnected with the Sn–Zn solder, various compounds are formed at the interconnection between the conductor and the solder during soldering and then gradually grow during energization heating at solid-state temperatures. Since such compounds may be brittle and will possess high electrical resistivities, their growth can deteriorate the mechanical and electrical properties of the interconnection.
The solid-state reactive diffusion in the Cu/(Sn–Zn) system was experimentally studied by Shohji et al.4) In their experiment, Cu/(Sn–Zn) diffusion couples were prepared from pure Cu and an eutectic Sn–Zn solder by a soldering technique and then isothermally annealed at temperatures of T = 373–423 K. According to their observation, the region with the composition Cu0.55Sn0.41Zn0.04 consisting of the Cu, β' and γ phases is formed at the original interface of the diffusion couple during annealing. Furthermore, the region with the composition Cu0.64Sn0.34Zn0.02 is produced at the interface between the Cu0.55Sn0.41Zn0.04 region and the Cu phase. Thus, rather complicated microstructure evolution takes place for the solid-state reactive diffusion in the Cu/(Sn–Zn) system. In order to understand the mechanism of such microstructure evolution, information on the solid-state reactive diffusion in the Cu/Sn and Cu/Zn systems is necessary.
For the Cu/Sn system, the kinetics of solid-state reactive diffusion was observed in a previous study.9) In this observation, Sn/Cu/Sn diffusion couples were prepared by a diffusion bonding technique and then isothermally annealed in the temperature range of T = 433–473 K. In this temperature range, an intermetallic layer composed of Cu6Sn5 and Cu3Sn is formed at the original Cu/Sn interface in the diffusion couple. The total thickness of the Cu6Sn5 and Cu3Sn layers increases in proportion to a power function of the annealing time. The exponent of the power function is close to 0.5 at T = 473 K but becomes 0.37 and 0.43 at T = 433 and 453 K, respectively. Thus, in the Cu/Sn system,9) the growth of the intermetallic layer is controlled by volume diffusion at T = 473 K but by volume and boundary diffusion at T = 433 and 453 K.
In contrast, the solid-state reactive diffusion in the Cu/Zn system was experimentally studied by Hoxha et al.10) In their study, Cu/Zn diffusion couples were prepared by a diffusion bonding technique and then isothermally annealed at temperatures of T = 523–653 K. Their study indicates that a compound layer consisting of the γ and ε phases is produced at the original interface of the diffusion couple during annealing. The total thickness of the γ and ε layers is almost proportional to the square root of the annealing time at T = 653 K. On the other hand, at T = 523–623 K, raw experimental values for thicknesses of the γ and ε layers are not indicated in their article.10) Nevertheless, they mention that the thickness rather linearly increases in proportion to the annealing time in the early stages at T = 523–623 K. This means that the layer growth is controlled by volume diffusion at T = 653 K but by interface reaction in the early stages at T = 523–623 K. Although the diffusion rate-controlling process will be realized also in the late stages at T = 523–623 K, reliable information on the rate-controlling process is lacking at these temperatures. To obtain such information, the kinetics of the solid-state reactive diffusion in the Cu/Zn system was experimentally observed in the temperature range of T = 523–623 K in the present study.
Sheet specimens with size of 20 mm × 7 mm × 1 mm were cut from a pure Cu commercial sheet with dimensions of 300 mm × 100 mm × 1 mm and purity of 99.96% and then separately annealed in evacuated silica capsules at 1173 K for 2 h, followed by air cooling without breaking the capsules. The two surfaces with area of 20 mm × 7 mm of each annealed Cu sheet specimen were mechanically polished on #800–4000 emery papers until a depth of 100 μm and then finished using diamond with diameter of 1 μm.
Sheet specimens with size of 12 mm × 5 mm × 1 mm were cut from a pure Zn commercial sheet with dimensions of 200 mm × 200 mm × 1 mm and purity of 99.5% and then separately annealed in evacuated silica capsules at 623 K for 2 h, followed by air cooling without breaking the capsules. The two surfaces with area of 12 mm × 5 mm of each annealed Zn sheet specimen were mechanically polished on #800 emery paper. One of the two polished surfaces was again mechanically polished on #1500–4000 emery papers until a depth of 100 μm and then finished using diamond with diameter of 1 μm.
After finishing, a Cu sheet specimen was immediately sandwiched between the finished surfaces of two freshly prepared Zn sheet specimens in ethanol by the technique used in a previous study.9) The sandwich Zn/Cu/Zn couples were completely dried and then heat treated for diffusion bonding in an evacuated silica tube at temperatures of 523 K, 573 K and 623 K for times of 2 h, 0.5 h and 0.5 h, respectively, followed by air cooling. After the heat treatment, the diffusion couples were isothermally annealed at 523 K, 573 K and 623 K for various times up to 47 h. The summation of the heat-treating and annealing times is hereafter merely called the annealing time t, and the annealing temperature is denoted by T. Cross-sections of the annealed diffusion couple were mechanically polished using diamond with diameters of 15 μm, 3 μm and 1 μm, and then finished with an OP-S liquid manufactured by Struers Ltd. The microstructure of the cross-section was observed by differential interference contrast optical microscopy (DICOM). Concentrations of Cu and Zn in each phase on the cross-section were measured by electron probe microanalysis (EPMA) using pure Cu and Zn with purity of 99.99% as standard specimens under the following conditions: the accelerating voltage was 20 kV; the probe current was 5 nA; the analyzing crystal was lithium fluoride (LiF) for Cu–Kα and Zn–Kα; and the chemical composition was evaluated by a standard ZAF correction technique.
A typical cross-sectional DICOM image of the diffusion couple annealed at T = 623 K for t = 1 h (3.6 ks) is shown in Fig. 1. For this DICOM image in Fig. 1, the top and bottom regions are the Zn and Cu specimens, respectively. As can be seen, layers with different contrasts are formed at the original Cu/Zn interface. To identify each layer, concentration profiles of Cu and Zn were measured by EPMA along the direction normal to the original interface. A result of the diffusion couple with T = 573 K and t = 7 h (25.2 ks) is indicated in Fig. 2. In this figure, the ordinate and the abscissa show the mol fraction yi of component i and the distance x measured from an arbitrary origin, respectively, and open circles and squares represent the mol fractions yCu and yZn, respectively. As can be seen, the layers on the Cu and Zn sides are the γ and ε phases, respectively. The thickness is smaller for the ε phase than for the γ phase. Similar results were obtained for all the diffusion couples annealed at T = 523–623 K. If we observe the edge of diffusion couple on the cross-section, we can find the location of the original Cu/Zn interface. This observation indicates that the γ and ε phases grow mainly into the Zn specimen but slightly towards the Cu specimen. Considering the mass conservation, we may expect that the Matano interface is located in the γ layer and thus migrates from the original interface towards the Zn side. According to a recent phase diagram in the binary Cu–Zn system,11) the β' phase as well as the γ and ε phases should appear as a stable intermediate phase at T = 523–623 K. However, the β' phase was not recognized in any annealed diffusion couples in the present study. For reactive diffusion in binary alloy systems, the growth rate of an intermediate phase is predominantly determined by the interdiffusion coefficient of the growing phase.12–22) If the interdiffusion coefficient of an intermediate phase is small at an experimental annealing temperature, the intermediate phase cannot grow to visible thicknesses within realistic annealing times.12–22) Consequently, the interdiffusion coefficient of the β' phase must be much smaller than those of the γ and ε phases. Furthermore, according to the results in Figs. 1 and 2, the interdiffusion coefficient has to be smaller for the ε phase than for the γ phase.
Cross-sectional DICOM image of diffusion couple annealed at T = 623 K for t = 1 h (3.6 ks).
Concentration profiles of Cu and Zn across compound layers in diffusion couple annealed at T = 573 K for t = 7 h (25.2 ks).
As shown in Fig. 1, a tow-phase layer consisting of the γ and ε phases is formed at the original Cu/Zn interface in the diffusion couple due to isothermal annealing at T = 523–623 K. Hereafter, the two-phase layer is merely called the intermetallic layer. From DICOM images, such as that indicated in Fig. 1, the area Aj of the intermetallic layer corresponding to the partial length wj of the original Cu/Zn interface was measured for cross-section j. The sums A and w were obtained by the equations9)
| \[ A = \sum_{j = 1}^{m} A_{j} \] | (1a) |
| \[ w = \sum_{j = 1}^{m} w_{j} \] | (1b) |
| \[ l = \frac{A}{w}. \] | (2) |
| \[ l = k \left( \frac{t}{t_{0}} \right)^n, \] | (3) |
The total thickness l of the intermetallic layer versus the annealing time t at T = 523, 573 and 623 K shown as open rhombuses, squares and circles, respectively.
According to Fig. 1, each compound is clearly distinguished in the intermetallic layer. From DICOM images, such as that shown in Fig. 1, the mean thickness li of compound layer i in the intermetallic layer was evaluated using the relationships similar to eqs. (1a), (1b) and (2), where i = 1 and 2 for the γ and ε phases, respectively. Thus, there exists the following relationship among l, l1 and l2.
| \[ l = l_{1} + l_{2} \] | (4) |
| \[ l_{i} = k_{i} \left( \frac{t}{t_{0}} \right)^n \] | (5) |
The thicknesses l, l1 and l2 versus the annealing time t shown as open circles, squares and rhombuses, respectively: (a) 523 K, (b) 573 K and (c) 623 K.
At each experimental annealing time, the ratio ri of the thickness li to the total thickness l was evaluated by the equation
| \[ r_{i} = \frac{l_i{}}{l}. \] | (6) |
The ratios r1 and r2 in eq. (6) versus the annealing time t shown as open circles and squares, respectively: (a) 523 K, (b) 573 K and (c) 623 K.
The ratios r1 and r2 in eq. (6) versus the annealing temperature T shown as open circles and squares, respectively, with error bars.
The values of n in Fig. 3 are plotted against T as open circles with error bars in Fig. 7. If the growth of the intermetallic layer is controlled by volume diffusion, n is equal to 0.5.12–22) On the other hand, n is equivalent to unity, if interface reaction governs the layer growth.23–28) According to the result in Fig. 7, n takes intermediate values between 0.5 and unity. This means that both volume diffusion and interface reaction contribute to the rate-controlling process of the layer growth at T = 523–623 K. Since the ratios r1 and r2 are constant independent of t at each annealing temperature as shown in Fig. 5, the same rate-controlling process works for both the γ and ε phases. Such a mixed rate-controlling process of solid-state reactive diffusion was observed for various metal systems in previous studies.23–28) The values n = 0.60–0.62 are closer to 0.5 than to unity, and hence the contribution of volume diffusion is more predominant than that of interface reaction. As previously mentioned, the intermetallic layer grows mainly towards the Zn side and merely slightly towards the Cu side. Therefore, the Zn/ε interface is mobile, but the Cu/γ interface is rather stationary. Consequently, it is plausible that the interface reaction at the mobile Zn/ε interface dominantly influences the rate-controlling process of the layer growth. As previously mentioned, on the basis of the mass conservation, it is expected that the Matano interface lies in the γ layer and thus migrates from the original interface towards the Zn side. If only volume diffusion is the rate-controlling process of the layer growth, the interdiffusion coefficient of each phase is determined by an appropriate method.29) Unfortunately, however, the mixed rate-controlling process governs the layer growth as mentioned earlier. Therefore, the interdiffusion coefficient cannot be determined in a straightforward manner.
The exponent n versus the annealing temperature T.
As mentioned in Section 1, the solid-state reactive diffusion in the Cu/Zn system was experimentally observed also by Hoxha et al.10) In their experiment, Cu/Zn diffusion couples were prepared by a diffusion bonding technique and then isothermally annealed at T = 523–653 K. According to their observation, a compound layer composed of the γ and ε phases is formed at the original interface of the diffusion couple during annealing. They reported the concentration profiles across the γ and ε phases in the diffusion couples annealed at T = 653 K for various periods. From such concentration profiles, we can measure the thicknesses l, l1 and l2. The values of l, l1 and l2 are plotted against the annealing time t as open circles, squares and rhombuses, respectively, in Fig. 8. Using the experimental points in Fig. 8, the values of k, k1, k2 and n in eqs. (3) and (5) were evaluated by the least-squares method as shown with various straight lines in a manner similar to Fig. 4. The evaluated values are shown in Fig. 8. As can be seen, n is close to 0.5. Therefore, we can conclude that the layer growth is predominantly controlled by volume diffusion at T = 653 K. In their article,10) the following equation is used to describe the relationship between li and t, and the values of K1 = 6257.5 × 10−12 m2/s and K2 = 1150.6 × 10−12 m2/s are estimated for l1 and l2, respectively, at T = 653 K.
| \[ l_{i}^2 = 2K_{i}t \] | (7) |
The thicknesses l, l1 and l2 versus the annealing time t at T = 653 K shown as open circles, squares and rhombuses, respectively, reported by Hoxha et al.10).
As shown in Fig. 7, n is rather insensitive to T. If n is considered to be independent of T, k and n in eq. (3) are simultaneously evaluated by the least-squares method from all the experimental points plotted in Fig. 3. The evaluated value of n is shown as a solid circle with error bars in Fig. 7, and those of k are indicated as open circles with error bars in Fig. 9. In Fig. 9, the ordinate shows the logarithm of k, and the abscissa indicates the reciprocal of T. The dependence of k on T is generally expressed by the following equation.30)
| \[ k = k_{0} \exp \left( - \frac{Q_{k}}{RT} \right) \] | (8) |
The proportionality coefficient k versus the annealing temperature T.
The solid-state reactive diffusion in the Cu/Zn system was experimentally observed using the Zn/Cu/Zn diffusion couples prepared by the diffusion bonding technique. The diffusion couples were isothermally annealed at temperatures of T = 523, 573 and 623 K for various times up to t = 49 h. During annealing, the γ + ε two-phase layer forms at the original Cu/Zn interface in the diffusion couple, where the thickness is smaller for the ε layer than for the γ layer. The total thickness of the two-phase layer is proportional to a power function of the annealing time. The exponent of the power function takes intermediate values between 0.5 and unity under the present annealing conditions. This means that both volume diffusion and interface reaction contribute to the rate-controlling process of the layer growth.
The present study was supported by the Iketani Science and Technology Foundation in Japan. The study was also partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
