Diffusion Induced Recrystallization Region Research Articles

Thermodynamics and kinetics of interdiffusion in Ni//NiAl diffusion couples

The growth behavior of Ni3Al after nucleation at the Ni/NiAl interface was investigated by using macroscopic diffusion couples at low annealing temperatures of 973–1073 K. The thickness and grain size of the Ni3Al phase at different annealing temperatures were statistically analyzed by scanning electron microscopy to evaluate the growth kinetics of the Ni3Al layer. According to the growth rate exponent, the growth of Ni3Al layer to NiAl is almost completely controlled by volume diffusion (VD) when it is above 1023 K, and by boundary diffusion (BD) when it is below 1023 K. In contrast, the growth of Ni3Al into Ni is controlled by VD almost whether at 1023 K or 1073 K. Remarkably, a continuous Al-rich Ni grain layer was formed at the Ni3Al/Ni interface by diffusion-induced recrystallization (DIR), and the experimental results for DIR region of composition and growth behavior were numerically analyzed using the thermodynamic and kinetic models, respectively. The analyses suggest that the composition of the DIR region in the Ni(Al) binary system can be determined by the thermodynamic conditions of the chemical driving force model (CDF model). Additionally, kinetic analysis using the new extended model (NE model) indicates that under current annealing conditions, interface reaction and BD control growth at the moving boundary of the DIR region. Furthermore, the temperature stability range of Ni5Al3 in the Ni//NiAl system was subjected to systematic analysis.

Study of the intermetallic growth in copper-clad aluminum wires after thermal aging

Study of the solid-state diffusion between copper and aluminum was carried out in the temperature range [573–673] K in order to better understand the aging mechanisms which occur in copper-clad aluminum thin wires. A complete microscopic analysis was performed to evaluate the interface composition and corresponding microstructure. The intermetallic phases developed during annealing identified by TEM and X-Ray diffraction analysis are respectively Al2Cu, AlCu, and Al4Cu9. A fine layer containing nanometric copper grains was also depicted and identified as a diffusion-induced recrystallization region. These results agree with EDXS analysis and nanoindentation measurements. The effective heat of formation model was used to evaluate the first phase(s) which happens in the interface and the sequence formation of intermetallic compounds during annealing. This model finely describes the metallurgical aging of copper-clad aluminum wires and explains the presence of only three intermetallic compounds in the interface between copper and aluminum.

Solid-state reactive diffusion between Ni and W

Various alloys are interconnected with W using a Ni intermediate layer by the diffusion bonding (DB) technique. During solid-state heating in the DB technique, however, reactive diffusion occurs at the interconnection between Ni and W. In order to examine the kinetics of the reactive diffusion, sandwich Ni/W/Ni diffusion couples were isothermally annealed at temperatures of T = 1023–1173 K for various times up to t = 366 h. Owing to annealing, Ni 4W is produced as a layer at the Ni/W interface in the diffusion couple and grows predominantly towards Ni. The thickness of the Ni 4W layer increases in proportion to a power function of the annealing time. The exponent of the power function is close to 0.5 at T = 1173 K and gradually decreases with decreasing annealing temperature. Furthermore, grain growth takes place in Ni 4W due to annealing. Therefore, volume diffusion is the rate-controlling process for the growth of Ni 4W at T = 1173 K. At T < 1173 K, however, boundary diffusion contributes to the rate-controlling process, and the contribution of boundary diffusion increases with decreasing annealing temperature. On the other hand, a region alloyed with W is formed in Ni from the Ni 4W/Ni interface by diffusion-induced recrystallization (DIR). The growth rate of the DIR region is much greater than the penetration rate of W into Ni by volume diffusion, and the concentration of W in the DIR region at the Ni 4W/Ni interface is equal to the solubility of W in Ni. Such growth behavior of the DIR region was numerically analyzed using a mathematical model. The analysis indicates that the growth of the DIR region is controlled by the interface reaction at the moving boundary of the DIR region as well as the boundary diffusion along the grain boundaries across the DIR region under the present annealing conditions.

Diffusion-induced recrystallization in the Cu(Pd) system at complete solid-solution temperatures

Owing to annealing at complete solid-solution temperatures around 1,000 K, Pd can quickly penetrate into Cu due to diffusion-induced recrystallization (DIR). To examine this penetration behavior, DIR in the Cu(Pd) system was experimentally observed in the present study. A diffusion bonding technique was used to prepare polycrystalline Cu/Pd/Cu diffusion couples. The diffusion couple was isothermally annealed at temperatures of T = 923–1,023 K for various times up to t = 176 h. During annealing, a region alloyed with Pd is produced in Cu from the Cu/Pd interface due to DIR. The concentration of Pd on the Pd-rich side in the DIR region remains almost constant independent of the annealing time but increases with increasing annealing temperature. On the other hand, the mean thickness of the DIR region increases with increasing annealing time. The growth rate of the DIR region is a monotonically increasing function of the annealing temperature. The experimental findings of the kinetics study were quantitatively analyzed using a mathematical model. The analysis satisfactorily reproduces the overall growth behavior of the DIR region.

Kinetics of Diffusion-Induced Recrystallization in the Cu(Ni) System at Low Temperatures

During annealing at temperatures around 800 K, Ni can quickly penetrate into Cu due to diffusion-induced recrystallization (DIR). To examine this penetration rate, the kinetics of DIR in the Cu(Ni) system was experimentally determined in the present study. Experiments were conducted using polycrystalline Cu/Ni/Cu diffusion couples which were prepared by a diffusion bonding technique. The diffusion couples were isothermally annealed at temperatures of T = 723 K to 823 K for various times up to t = 144 h. During annealing, a region alloyed with Ni is formed in Cu from the Cu/Ni interface due to DIR. The concentration of Ni on the Ni-rich side in the DIR region remains almost constant independent of the annealing time, but gradually increases with increasing annealing temperature. However, the mean thickness of the DIR region increased with increasing annealing time. The growth rate of the DIR region is a monotonically increasing function of the annealing temperature. The experimental findings of the kinetics study were quantitatively analyzed using a mathematical model. The analysis indicates that the growth of the DIR region is controlled by the interface reaction at the moving boundary of the DIR region as well as the boundary diffusion along the grain boundaries across the DIR region.

Orientation Relationship for Fine Grains Formed by Diffusion-Induced Recrystallization in the Ni(Cu) System

In order to examine the crystallography for diffusion-induced recrystallization (DIR) in the Ni(Cu) system, Cu/Ni/Cu diffusion couples were prepared by a diffusion bonding technique from a pure Cu single-crystal specimen and a pure Ni polycrystalline specimen, and then isothermally annealed at a temperature of 923 K for various times of 1–60 h. The Miller indices of the Cu specimen along the Cu/Ni interface are (111). The notation A(B) means that a solute B diffuses into a pure metal A or a binary A–B alloy with the A-rich single-phase microstructure. Due to DIR during annealing, a region with fine grains alloyed with Cu is produced into the Ni specimen from the Cu/Ni interface in the diffusion couple. The orientation relationship between the fine grain in the DIR region and the Cu or Ni specimen was analyzed by an electron backscattered diffraction technique as well as transmission electron microscopy. Orientation relationships close to but not identical to the cube/ cube relationship exist between the Cu specimen and many fine grains in the DIR region. The chemical driving force for the formation of the DIR region, the boundary energy and the boundary diffusion coefficient were evaluated by mathematical models. According to the evaluation, it is likely that fine grains surrounded by small-angle boundaries are formed and grow moderately during DIR. [doi:10.2320/matertrans.MRA2007197]

Fast Penetration of Sn into Ag by Diffusion Induced Recrystallization

At interconnection between a Ag-base conductor alloy and a Sn-base solder alloy, fast penetration of Sn into the conductor alloy occurs due to diffusion induced recrystallization (DIR) during solid-state heating under usual energization conditions. Like formation of binary Ag–Sn compounds, the penetration of Sn deteriorates the electrical conductivity at the interconnection. In order to examine the penetration rate of Sn into the conductor alloy, the kinetics of DIR in the Ag(Sn) system was experimentally observed in the present study. The experiment was carried out using Sn/Ag/Sn diffusion couples prepared by a diffusion bonding technique. The diffusion couples were isothermally annealed at temperatures of T ¼ 433{473 K for various times up to t ¼ 1100 h in an oil bath with silicone oil. Due to annealing, a region alloyed with Sn is formed in Ag due to DIR at T ¼ 453 and 473 K. At T ¼ 433 K, however, the DIR region could not be recognized clearly. The concentration of Sn in the DIR region is about half of the solubility of Sn in Ag. The mean thickness l of the DIR region reaches to 4 mm for t ¼ 1100 ha t T ¼ 453 K and 5 mm for t ¼ 890 ha tT ¼ 473 K. The experimental results were theoretically analyzed using mathematical models. The analysis indicates that the growth of the DIR region is controlled by the interface reaction at the moving boundary of the DIR region within the experimental annealing times. At longer annealing times, however, the interface reaction is no longer the bottleneck for migration of the moving boundary and the grain boundary diffusion across the DIR region governs the growth of the DIR region.

Kinetic features of diffusion induced recrystallization in the Cu(Ni) system at 873 K

The kinetics of diffusion induced recrystallization (DIR) in the Cu(Ni) system was experimentally studied at 873 K. Ni/(CuNi)/Ni diffusion couples were prepared by a diffusion bonding technique using a pure Ni specimen and binary CuNi alloys with mol fractions of Ni of y 0=0, 0.114 and 0.231, and then annealed at 873 K for various times between 1 and 72 h (3.6×10 3 and 2.59×10 5 s). After annealing, a fine grain region (DIR region) alloyed with Ni was observed to form at the interface owing to DIR and to grow mainly towards the Cu phase. The thickness l of the DIR region monotonically increases with increasing annealing time t according to the relationship l= k( t/ t 0) n , where t 0 is unit time, 1 s. The exponent n takes a constant value of 0.45 independent of the composition y 0. On the other hand, as the composition y 0 increases from 0 to 0.231, the proportionality coefficient k decreases from 5.7×10 −8 to 4.5×10 −8 m. The experimental results were theoretically analyzed using a kinetic model proposed by the present authors. The growth behavior of the DIR region was explained well by the analysis. This means that the chemical driving force due to the compositional difference between the Cu phase and the DIR region is the most important driving force for DIR in the Cu(Ni) system under the present experimental conditions.

Observations on diffusion-induced recrystallization in binary Ni/Cu diffusion couples annealed at an intermediate temperature

Diffusion-induced recrystallization (DIR) was experimentally studied using diffusion couples consisting of a pure Cu single crystal and a binary Ni–Cu polycrystalline alloy. The (Ni–Cu)/Cu diffusion couples were annealed at 873 K for various times between 1 and 72 h (3.6×10 3 and 2.59×10 5 s). During annealing, a fine grain region (DIR region) was observed to form at an interface of each diffusion couple due to DIR and to grow mainly towards the Cu phase. The thickness l of the DIR region increases with increasing annealing time t according to the relationship l= k l ( t/t 0) n , where t 0 is unit time, 1 s. The proportionality coefficient and the exponent take constant values of k=2.18×10 −8 m and n=0.55, respectively, independent of the composition of the Ni phase within experimental uncertainty. The compositional differences across the moving boundaries of the DIR region on both the Cu phase and Ni phase sides decrease in inverse proportion to the almost fourth root of the annealing time. At each annealing time, the compositional difference Δ x c on the Ni phase side monotonically decreases with increasing Cu concentration x 0 in the Ni phase, whereas there is no clear relationship between the compositional difference Δ x i on the Cu phase side and the Cu concentration x 0.

Numerical Analysis of Observations on Diffusion Induced Recrystallization in the Ni(Cu) System using A Kinetic Model

Considering the effect of the friction force due to volume diffusion of a solute on the driving force, a new kinetic model has been proposed for diffusion induced recrystallization (DIR) in the A(B) system in which solute B atoms diffuse into a pure A metal or a binary A-B alloy. The energy balance model [M. Kajihara and W. Gust: Scr. Mater. 38 (1998) 1621] has been combined with the columnar geometry and boundary diffusion model [C. Li and M. Hillert: Acta Metall. 29 (1981) 1949] and the extended model [Y. Kawanami et al.: ISIJ Int. 37 (1997) 921] in order to describe mathematically the growth rate of the fine grain region (DIR region) formed by DIR as a function of the reaction time. DIR in the Ni(Cu) system was experimentally observed by Kawanami et al. [Y. Kawanami et al.: Mater. Trans., JIM 39 (1998) 218] at 923 and 1023 K. The new model has been utilized to analyze their observations theoretically. According to the observations, the migration rate v of the moving boundary gradually decreases with increasing reaction time. However, the decrease in the migration rate v is negligible during a small time interval of Δt = 1 s at the experimental reaction times. Thus, the value of v was assumed to be constant at each time step with At = 1 s in order to simplify the analysis. Using the mobility M of the moving boundary as the fitting parameter, the thickness of the DIR region was calculated as a function of the reaction time by a numerical technique. The calculation gives values of M = 3.73 x 10 -17 and 1.51 x 10 -15 m 4 /Js at 923 and 1023 K, respectively, and thus M 0 = 1.03 m 4 /Js and Q M = 290 kJ/mol for M = M 0 exp(-Q M /RT). The temperature dependence of the mobility indicates that the grain boundary migration may be governed by the solute drag effect for which the volume diffusion of the solute along the moving direction in the untransformed matrix ahead of the moving boundary has the most important role.

Growth behavior of fine grains formed by diffusion induced recrystallization in the Cu(Zn) system

The growth behavior of fine grains produced due to diffusion induced recrystallization (DIR) was experimentally studied for the Cu(Zn) system using single crystal Cu specimens. The Cu specimens were annealed at 693 K for various times together with a Zn source alloy by a capsule zincification technique and then DIR was observed to take place on the surfaces of the specimens. The DIR region consists of an almost single layer of fine grains. Although the average height l and the average diameter s of the fine grains increase with increasing annealing time, the aspect ratio s/ l is kept to be nearly unity during annealing. The Zn concentration on the specimen surface is smaller than that in the Zn source alloy at early stages of the reaction. Such lower Zn concentrations could be explained using the maximum driving force model proposed by Kajihara and Gust ( Acta metall. mater., 1991, 39, 2565). The composition on the specimen surface gradually approaches the equilibrium value with increasing annealing time. This means that the amount of the Zn source alloy is large enough to maintain the supply of Zn atoms to the specimen in each zincification capsule. The kinetic model by Li and Hillert ( Acta metall., 1981, 29, 1949) and the extended model by Kawanami et al. ( ISIJ Int., 1997, 37, 921) could rather well reproduce the annealing time dependence of the growth rate of the DIR region. The contribution of volume diffusion to the transfer of Zn atoms from the surface to the moving boundaries in the DIR region was estimated to be negligible. Thus, the chemical driving force is considered to be the most important driving force for the grain boundary migration and the boundary diffusion along the grain boundaries in the DIR region is recognized to be the rate controlling process of DIR.

Microstructure Observations for Diffusion Induced Recrystallization and Diffusion Induced Grain Boundary Migration on Surfaces of Zincified Cu Bicrystals With [1 1 0] Twist Boundaries

The formation behavior of the fine-grain region alloyed with Zn due to diffusion induced recrystallization (DIR) in the Cu(Zn) system was experimentally examined for the surfaces polished in different manners using a Cu bicrystal containing a [1 1 0] twist boundary with a misorientation angle of θ = 46° zincified at 673 K for 2.88 × 104 s with Cu-15 wt% Zn and Cu-30 wt% Zn alloys by a capsule zincification technique. The extent and morphology of the fine-grain DIR region vary depending on the surface conditions and the composition of the Zn-source Cu-Zn alloy. For the specimen with the surface electrolytically polished in an etchant consisting of 20 vol% of nitric acid and 80 vol% of methanol, no DIR region was formed on the whole surface when the Cu-15 wt% Zn alloy was used as a Zn source.

Fast Penetration of Cu in Ni of Cu/Ni/Cu Diffusion Couples Due to Diffusion Induced Recrystallization.

Rapid penetration of Cu in Ni owing to diffusion induced recrystallization (DIR) in the Ni(Cu) system was experimentally examined using the Cu/Ni/Cu diffusion couples consisting of pure Cu single crystals and a pure Ni polycrystalline specimen annealed at 923 and 1 023 K in previous studies. The experimental results have been theoretically analyzed to find a new criterion for the occurrence of DIR in the present study. According to the experimental results, the thickness l of the DIR region in the Ni phase increases in proportion to the square root of the annealing time t. Thus, if we define the parameter D h as the hypothetical diffusion coefficient which gives the overall penetration rate of Cu across the DIR region, the thickness l is described as a function of the annealing time t by the equation l=2√D h t. The temperature dependence of D h has been obtained from the experimental results and then compared with that of the volume diffusion coefficient D v of Cu in Ni. From the comparison, it is concluded that the ratio D h /D v should be greater than thirty in order for DIR to take place in the Ni(Cu) system.

Growth Rate of Fine Grains Formed by Diffusion Induced Recrystallization in Ni Layer of Cu/Ni/Cu Diffusion Couples

Diffusion induced recrystallization (DIR) in the Ni(Cu) system was experimentally studied. The notation Ni(Cu) means that Cu atoms diffuse into a pure Ni or binary Ni-Cu phase. The Cu/Ni/Cu diffusion couples consisting of pure Cu single crystals with the same crystallographic orientation and a pure Ni polycrystalline specimen were annealed at 923 and 1023 K for various times between 1.8 × 10 3 and 1.76 × 10 5 s. The penetration of Cu in the Ni phase was found to occur at rates three orders of magnitude greater than the ones evaluated from the volume diffusion. This unusually rapid penetration is due to DIR. DIR was observed to take place only in the Ni phase from the interfaces in all the diffusion couples annealed at 923 and 1023 K. The observations indicate that the thickness I of the DIR region increases with increasing annealing time t according to the relationships l=4.9 × 10 -8 (t/t 0 ) 0.41 and l=1.8 × l0 -7 (t/t 0 ) 0.37 at 923 and 1023 K, respectively. Here, I and t are measured in m and s, respectively, and t 0 is unit time, 1 s. The analysis using the kinetic equation proposed by Li and Hillert could account for the observations quantitatively.

Analysis of Kinetics of Diffusion Induced Recrystallization in Fe Phase of Cu/Fe/Cu Diffusion Couples.

Combining the columnar-geometry and boundary-diffusion model by Li and Hillert with the energy balance model by Kajihara and Gust, a new kinetic equation has been obtained to describe the growth rate of the alloyed region due to diffusion induced recrystallization (DIR) in a solution phase of binary systems. The equation has been utilized to analyze quantitatively the kinetics of DIR in the Fe(Cu) system observed by the present authors using Cu/(Fe-4.8mass%)/Cu diffusion couples. The notation Fe(Cu) means that Cu atoms diffuse into a pure Fe or binary Fe-Cu phase. The observations indicate that the thickness l of the DIR region formed in the Fe phase from each interface increases with increasing annealing time t according to the relationship l=1.58 x 10 -6 (t/t 0 ) 0.29 at 1323 K. Here, l and t are measured in m and s, respectively, and t 0 is unit time, 1 s. Using the mobility M as the fitting parameter of the kinetic equation, we have obtained the value of M=8.64 x 10 -13 m 4 /J s and the relationship l= 1.08 x 10 -6 (t/t 0 ) 0.33 on the basis of the observations. Through the analysis, it is concluded that l increases in proportion to √t for DIR in a pure metal whereas l increases proportionately with 3 √t for DIR in a solution phase even with a low solute concentration.

Experimental Study on Diffusion Induced Recrystallization in Cu/Fe/Cu Diffusion Couples Using Cu Single Crystals.

Diffusion induced recrystallization (DIR) in a face-centered-cubic (f.c.c.) Fe phase was experimentally studied in the Fe(Cu) system. The notation Fe(Cu) means that Cu atoms diffuse into a pure Fe or binary Fe-Cu phase. The Cu/Fe/Cu and Cu/(Fe-4.8Cu)/Cu diffusion couples consisting of a polycrystalline Fe phase specimen and pure Cu single crystals with the same crystallographic orientation were annealed at 1 193 and 1 323 K for various times between 3.0 x 10 2 and 8.6 x 10 4 s. The penetration of Cu in the f.c.c. Fe phase was found to occur at rates 100 times greater than the one evaluated from the volume diffusion. This unusually rapid penetration is due to DIR, which takes place in the Fe phase from the interfaces of the diffusion couples. DIR was observed to occur only in the Cu/(Fe-4.8Cu)/Cu diffusion couples annealed at 1 323 K under the present experimental conditions. The thickness w of the Fe phase decreases with increasing annealing time t according to the equation w/w o = 1 - 7.09 x 10 -8 (√t/w o ), whereas the thickness l of the DIR region increases with increasing annealing time according to the equation l=1.58x 10 -6 (t/t o ) 0.29 . Here, w o is the initial thickness of the Fe phase, and to is unit time, l s. The thicknesses w, w o and l are measured in m, and the annealing time t is measured in s.