Kinetics Of Reactive Diffusion Research Articles

Kinetics of Reactive Diffusion in the Co/Zn System at Solid-State Temperatures

Kinetics of Reactive Diffusion in the Co/Zn System at Solid-State Temperatures

Kinetics of Reactive Diffusion in the (Sn–Cu)/Ni System at Solid-State Temperatures

The kinetics of solid-state reactive diffusion in the (Pd-Cu)/Sn system was experimentally observed to examine how adding Cu into Pd influenced the growth behavior of compounds at the junction between the Sn-base solder and the multilayer Pd/Ni/Cu conductor during energization heating. In our experiment, Sn/(Pd-Cu)/Sn diffusion couples with Cu mole fractions (y) of 0.243, 0.497, and 0.735 were isothermally annealed at temperatures of 433 K to 473 K for various times up to 385 h. Annealing caused an intermetallic layer of rather uniform thickness to form between the Sn and Pd-Cu specimens in the diffusion couple. The intermetallic layer consisted of PdSn4, PdSn3, PdSn2, and Cu6Sn5 for y = 0. 243. However, PdSn3 and PdSn2 were not clearly detected for y = 0.497 or 0.735. The total thickness of the intermetallic layer was proportional to a power function of the annealing time, with the exponent of the power function being 0.33 to 0.53. Cases where the exponent was smaller than 0.5 indicated that boundary diffusion controlled the growth of the intermetallic layer. Cases where the exponent was equal to 0.5 implied that volume diffusion was the rate-controlling process. Even for exponents close to 0.5, however, the grain growth behavior of the intermetallic layer suggested that the layer growth was governed by boundary diffusion. For the annealing times tested in this work, the overall growth rate of the intermetallic layer was insensitive to the Cu concentration at y 0.75. As a consequence, the growth of compounds at the Pd junction in the multilayer Pd/Ni/Cu conductor was markedly decelerated by adding Cu when y > 0.75.

Kinetics of Reactive Diffusion in the (Pd-Cu)/Sn System at Solid-State Temperatures

The kinetics of solid-state reactive diffusion in the (Pd-Cu)/Sn system was experimentally observed to examine how adding Cu into Pd influenced the growth behavior of compounds at the junction between the Sn-base solder and the multilayer Pd/Ni/Cu conductor during energization heating. In our experiment, Sn/(Pd-Cu)/Sn diffusion couples with Cu mole fractions (y) of 0.243, 0.497, and 0.735 were isothermally annealed at temperatures of 433 K to 473 K for various times up to 385 h. Annealing caused an intermetallic layer of rather uniform thickness to form between the Sn and Pd-Cu specimens in the diffusion couple. The intermetallic layer consisted of PdSn4, PdSn3, PdSn2, and Cu6Sn5 for y = 0. 243. However, PdSn3 and PdSn2 were not clearly detected for y = 0.497 or 0.735. The total thickness of the intermetallic layer was proportional to a power function of the annealing time, with the exponent of the power function being 0.33 to 0.53. Cases where the exponent was smaller than 0.5 indicated that boundary diffusion controlled the growth of the intermetallic layer. Cases where the exponent was equal to 0.5 implied that volume diffusion was the rate-controlling process. Even for exponents close to 0.5, however, the grain growth behavior of the intermetallic layer suggested that the layer growth was governed by boundary diffusion. For the annealing times tested in this work, the overall growth rate of the intermetallic layer was insensitive to the Cu concentration at y 0.75. As a consequence, the growth of compounds at the Pd junction in the multilayer Pd/Ni/Cu conductor was markedly decelerated by adding Cu when y > 0.75.

Kinetics of Solid-State Reactive Diffusion between Au and Al

In the wire bonding technique, a thin Au wire is interconnected with an Al layer on a Si chip. During energization heating at solid-state temperatures, however, brittle Au-Al compounds with high electrical resistivities are formed at the interconnection by the reactive diffusion between Au and Al. In order to examine the growth behavior of the Au-Al compounds, the kinetics of the reactive diffusion was experimentally observed using sandwich Al/Au/Al diffusion couples. The diffusion couple was prepared by a diffusion bonding technique and then isothermally annealed at temperatures of 623–723 K for various times up to 103 h. Under such annealing conditions, the diffusion couple is practically considered semi-infinite. Owing to annealing, compound layers consisting of AuAl2, AuAl and Au8Al3 are produced at the initial Au/Al interface in the diffusion couple. The volume fraction in the compound layers is larger for Au8Al3 than for AuAl and AuAl2 in the early stages but becomes smaller for Au8Al3 than for AuAl and AuAl2 in the late stages. However, there are no systematic dependencies of the volume fraction on the annealing time and temperature. The total thickness of the compound layers is proportional to a power function of the annealing time. The exponent of the power function is smaller than 0.5 at 673–723 K. The exponent smaller than 0.5 means that the interdiffusion across the compound layers governs the layer growth and boundary diffusion predominantly contributes to the interdiffusion. On the other hand, at 623 K, the exponent is equal to unity for annealing times shorter than 8 h but smaller than 0.5 for those longer than 8 h. The exponent of unity indicates that the layer growth is controlled by the interface reaction at the migrating interface. Thus, at T=623 K, the transition of the rate-controlling process occurs at a critical annealing time of 8 h.

Kinetics of isothermal reactive diffusion between solid Fe and liquid Al

The kinetics of the reactive diffusion between solid Fe and liquid Al was experimentally observed using Fe/Al diffusion couples. The diffusion couples were prepared by an isothermal bonding technique and then immediately annealed in the temperature range of T = 1053–1093 K for various times up to t = 600 s. Owing to annealing, an intermetallic layer with a rather uniform thickness is produced at the Fe/Al interface in the diffusion couple and grows into the solid Fe specimen. The intermetallic layer consists of Fe2Al5 and FeAl3, and the thickness is much smaller for FeAl3 than for Fe2Al5. Hence, the growth of the intermetallic layer is predominantly governed by Fe2Al5. The total thickness, l, of the intermetallic layer increases with increasing annealing time, t, according to the parabolic relationship l 2 = Kt. This may mean that the growth of the intermetallic layer is controlled by volume diffusion. If the temperature dependence of the parabolic coefficient K is expressed by the equation K = K 0exp(−Q K /RT), K 0 = 126 m2/s and Q K = 248 kJ/mol are obtained from the experimental values of K at T = 1053–1093 K by the least-squares method. A mathematical model was used to evaluate the interdiffusion coefficient, D, of Fe2Al5 from K. The evaluation provides D 0 = 2.55 × 103 m2/s and Q = 259 kJ/mol for the dependence of D on T described as D = D 0exp(−Q/RT). Thus, K is one fifth of D at T = 1053–1093 K, and Q K does not necessarily coincide with Q. D is about two orders of magnitude greater for the values evaluated in the present study than for those extrapolated from the previously reported result at T = 823–913 K. The microstructure observation in a previous study suggests that such large values of D are attributed to the boundary diffusion in the intermetallic layer as well as the crystallographic anisotropy of Fe2Al5.

Kinetics of reactive diffusion between Ta and Cu–9.3Sn–0.3Ti alloy

Tantalum is used as a diffusion barrier in the superconducting Nb3Sn composite-wire manufactured by the bronze method. In order to examine the consumption behavior of the Ta barrier during annealing in the bronze method, the kinetics of the reactive diffusion between Ta and a bronze was experimentally observed using sandwich diffusion couples composed of Ta and a Cu–9.3Sn–0.3Ti alloy. The (Cu–Sn–Ti)/Ta/(Cu–Sn–Ti) diffusion couples were isothermally annealed at temperatures of T = 973–1053 K for various times up to t = 1462 h. Owing to annealing, Ta9Sn is formed as a uniform layer at the initial (Cu–Sn–Ti)/Ta interface in the diffusion couple, and gradually grows mainly toward Ta. The mean thickness of the Ta9Sn layer is proportional to a power function of the annealing time. However, the exponent of the power function is equal to unity at t tc. Thus, the transition of the rate-controlling process for the growth of Ta9Sn occurs at t = tc. The critical annealing time tc takes values of 1.83 × 106, 4.63 × 105, and 5.98 × 105 s at T = 973, 1023, and 1053 K, respectively. The growth of Ta9Sn is controlled by the interface reaction at the migrating Ta9Sn/Ta interface in the early stages with t tc. Due to the transition of the rate-controlling process, the growth rate is always much smaller for Ta9Sn than for Nb3Sn. As a result, Ta works as an effective barrier against the diffusion of Sn from the bronze to the Cu stabilizer in the superconducting Nb3Sn composite-wire.

Influence of Pd on kinetics of solid-state reactive diffusion between Sn and Ni

In order to examine the growth behavior of compounds at the interconnection between the Sn-base solder and the multilayer Pd/Ni/Cu conductor during energization heating, the influence of Pd on the kinetics of the reactive diffusion between Sn and Ni was experimentally observed at solid-state temperatures. In the experiment, diffusion couples consisting of pure Ni and binary Sn–Pd alloys with Pd concentrations of 1 at.%, 3 at.% and 5 at.% were prepared by a diffusion bonding technique, and then isothermally annealed at temperatures of 453 K and 473 K for various times up to 768 h. At these annealing temperatures, the Sn–Pd alloy is composed of the β–Sn matrix dispersed with coarse blocks of PdSn 4. During annealing, compound layers of (Pd, Ni)Sn 4 and Ni 3Sn 4 are formed at the (Sn–Pd)/Ni interface in the diffusion couple. The thickness is slightly greater for (Pd, Ni)Sn 4 than for Ni 3Sn 4. The square of the total thickness of the compound layers is proportional to the annealing time. Hence, the growth of the compound layers is controlled by volume diffusion. The proportionality coefficient is one order of magnitude greater for 1–5 at.% Pd than for 0 at.% Pd. Consequently, PdSn 4 in the Sn-base solder considerably accelerates the solid-state reactive diffusion between the solder and the Ni layer of the Pd/Ni/Cu conductor during energization heating.

Kinetics of reactive diffusion between Pd–Ag alloys and Sn at solid-state temperatures

Abstract In order to examine the influence of Ag on the growth behavior of compounds at the interconnection between the Sn-base solder and the multilayer Pd/Ni/Cu conductor during energization heating, the kinetics of the reactive diffusion in the (Pd–Ag)/Sn system was experimentally studied at solid-state temperatures. Diffusion couples consisting of pure Sn and binary Pd–Ag alloys with concentrations of 25 and 50 at.% Ag were prepared by a diffusion bonding technique, and then isothermally annealed in the temperature range between T = 433 and 473 K for various times up to 312 h. During annealing, a PdSn 4 compound layer dispersed with fine particles of Ag 3 Sn is formed at the (Pd–Ag)/Sn interface in the diffusion couple. The square of the mean thickness l of the compound layer is proportional to the annealing time t as follows: l 2 = Kt , where K is the parabolic coefficient. Since the grain size of PdSn 4 monotonically increases with increasing annealing time, the growth of the compound layer is controlled by volume diffusion in each phase. The value of K becomes less than half due to addition of Ag with 50 at.% into Pd. Hence, the addition of Ag into the Pd layer inhibits the deterioration of the electrical and mechanical properties at the interconnection between the Sn-base solder and the multilayer Pd/Ni/Cu conductor during energization heating.

Influence of Temperature Dependence of Solubility on Kinetics for Reactive Diffusion in a Hypothetical Binary System

Influence of temperature dependence of solubility for each phase on kinetics of reactive diffusion has been theoretically analyzed for a hypothetical binary system consisting of two primary solid-solution phases (� and � ) and one compound phase (� ). For the analysis, we consider that thephase is produced owing to the reactive diffusion between theandphases in a semi-infinite diffusion couple and the growth of the � phase is controlled by volume diffusion. In such a case, the parabolic relationship holds good between the thickness l of thephase and the annealing time t as follows: l 2 ¼ Kt. Here, the parabolic coefficient K is mathematically expressed as a function of the interdiffusion coefficients and the solubility ranges of the � , � andphases. The temperature dependencies of the parabolic coefficient K, the solubility rangey � and the interdiffusion coefficient Dof the � (� ¼ �; �; � ) phase are described by Arrhenius equations of K ¼ K0 expð� QK =RTÞ, � y � ¼ � yexpð� Q � =RTÞ and D � ¼ Dexpð� Q �=RTÞ, respectively. The analysis indicates that QK is close to Q � þ Qat Q � � Qand Q � � Qbut greater than Q � þ Qat Q � > Qor Q � > Q �. As a consequence, the temperature dependency of the parabolic coefficient is directly related with those of the interdiffusion coefficient and the solubility range of the compound phase in the former case but not in the latter case. (doi:10.2320/matertrans.MRA2007316)

Quantitative analysis for kinetics of reactive diffusion in the Fe–Cr system

In the binary Fe–Cr system, the γ phase with the face-centered cubic structure becomes a stable intermediate phase sandwiched between the Fe-rich α1 and Cr-rich α2 phases with the body-centered cubic structure in the temperature range between T = 1,119 and 1,185 K. Within this temperature range, the reactive diffusion between the α1 and α2 phases was experimentally observed by Nishizawa and Chiba (Nishizawa and Chiba (1970) J Jap Inst Met 34:629). In their experiment, Fe/Cr diffusion couples were annealed at T = 1,123–1,163 K for up to 600 h. Although the γ phase should be formed due to annealing, it was not recognized in any annealed diffusion couples. The mathematical model reported in a previous study (2004 Acta Mater 52:1193) was used to analyze their experimental results theoretically. In order to provide the boundary conditions for the analysis, the phase diagram in the Fe–Cr system was computed by a CALPHAD technique. The analysis indicates that the γ phase is actually produced at the interface but its thickness is less than 1 μm even after annealing at T = 1,163 K for 600 h. Thus, the γ phase is practically invisible under their experimental conditions. The analysis provides the experimental conditions for the γ phase to grow to observable thicknesses.

Numerical analysis for migration of interface between liquid and solid phases during reactive diffusion in the binary Cu–Al system

The kinetics of reactive diffusion was experimentally examined for the binary Cu–Al system using Cu/Al diffusion couples initially consisting of pure Cu and Al in a previous study. The diffusion couple was isothermally annealed at temperatures of T = 973–1073 K. During annealing, compound layers of the β, γ and ɛ phases are formed between the Cu-rich solid (α) and Al-rich liquid (L) phases, and the L/ɛ interface migrates towards the ɛ phase. The migration rate of the L/ɛ interface is much greater than the overall growth rate of the compound layers, and there exists the parabolic relationship between the migration distance and the annealing time. This means that the interdiffusion in the solid phases is negligible and the migration of the interface is controlled by the interdiffusion in the L phase. The parabolic relationship may hold good only in a semi-infinite diffusion couple. Within the experimental annealing times, however, overlap of diffusion field occurs in the L phase, and thus the diffusion couple becomes finite. In order to account for the experimental result, the migration behavior of the L/ɛ interface in the finite Cu/Al diffusion couple was numerically analyzed using a mathematical model. The analysis yields that the parabolic relationship holds good within experimental uncertainty even in a finite diffusion couple on condition that volume diffusion is the rate-controlling process and overlap of diffusion field lightly takes place in each phase.

Kinetics of reactive diffusion between Cu–8.1Sn–0.3Ti alloy and Nb

The kinetics of the reactive diffusion between a ternary Cu–8.1 at.% Sn–0.3 at.% Ti alloy and pure Nb was experimentally examined in a metallographical manner. In the experiment, sandwich (Cu–Sn–Ti)/Nb/(Cu–Sn–Ti) diffusion couples were isothermally annealed in the temperature range between T = 923 and 1053 K for various periods up to 604 h. During annealing, the Nb 3Sn compound is produced as a layer along each (Cu–Sn–Ti)/Nb interface in the diffusion couple. The Nb 3Sn layer grows predominantly towards Nb but scarcely towards the Cu–Sn–Ti alloy. This means that the growth of the Nb 3Sn layer is governed by the migration of the Nb 3Sn/Nb interface. The mean thickness l of the Nb 3Sn layer is expressed as a power function of the annealing time t by the equation l = k( t/t 0) n . Here, t 0 is unit time, 1 s. The exponent n is nearly equal to unity at T = 923–973 K and monotonically decreases from 0.9 to 0.7 with increasing annealing temperature from T = 973 to 1053 K. Thus, the interface reaction at the migrating Nb 3Sn/Nb interface is the rate-controlling process for the growth of the Nb 3Sn layer at T = 923–973 K and the interdiffusion across the Nb 3Sn layer as well as the interface reaction contributes to the rate-controlling process at T = 973–1053 K. The volume diffusion in the Nb 3Sn layer may govern the interdiffusion at T = 1053 K, but the grain boundary diffusion along grain boundaries in the Nb 3Sn layer will contribute to the interdiffusion at T = 923–1023 K.

Kinetics of reactive diffusion in the (Au–Ni)/Sn system at solid-state temperatures

The kinetics of the reactive diffusion in the ternary (Au–Ni)/Sn system was experimentally studied at solid-state temperatures. Binary Au–Ni alloys containing 10 and 20 mass% of Ni were used to prepare sandwich Sn/(Au–Ni)/Sn diffusion couples by a diffusion bonding technique. The diffusion couples were isothermally annealed at temperatures of T = 433, 453 and 473 K for various times up to 1246 h. Due to annealing, Au 1.5Ni 0.5Sn 8 and AuNi 2Sn 4 compound layers are formed along the (Au–Ni)/Sn interface in the Au–20Ni diffusion couple, but Au 1.7Ni 0.3Sn 8, AuSn 2 and Au 6Ni 4Sn 15 compound layers dispersed with fine particles of AuNi 2Sn 4 are produced along the interface in the Au–10Ni diffusion couple. The total thickness l of the compound layers 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. For both diffusion couples, the exponent n increases with decreasing annealing temperature. However, for the Au–20Ni diffusion couple, n is close to 0.5 at T = 453–473 K, and takes a value of 0.7 at T = 433 K. This means that volume diffusion is the rate-controlling process for the growth of the compound layers at higher annealing temperatures, but interface reaction contributes to the rate-controlling process at lower annealing temperatures. On the other hand, for the Au–10Ni diffusion couple, n is smaller than 0.5 at T = 453–473 K, but close to 0.5 at T = 433 K. The values n < 0.5 indicate that grain boundary diffusion as well as volume diffusion contributes to the rate-controlling process and grain growth occurs at certain rates in the compound layers. Consequently, for the reactive diffusion in the ternary (Au–Ni)/Sn system, the rate-controlling process considerably varies depending on the composition of the Au–Ni alloy and the annealing temperature.

Kinetics of reactive diffusion between Au and Sn during annealing at solid-state temperatures

Abstract The reactive diffusion between Au and Sn was experimentally studied at solid-state temperatures using Sn/Au/Sn diffusion couples prepared by a diffusion bonding technique. The diffusion couples were annealed at temperatures of T = 393 and 473 K for various times in an oil bath with silicone oil. After annealing, compound layers composed of AuSn4, AuSn2 and AuSn were recognized to form at the Au/Sn interface. The thickness of the AuSn4 layer is about six and four times greater than those of the AuSn2 and AuSn layers at T = 393 and 473 K, respectively. The ratio of the thicknesses of the compound layers is kept constant independently of the annealing time. The total thickness l of the compound layers is described as a function of the annealing time t by the equation l = k(t/t0)n, where t0 is unit time, 1 s. The exponent n is nearly equal to 1/2 at T = 393 K but takes a value between 1/4 and 1/2 at T = 473 K. Such an intermediate value of n at T = 473 K indicates that the grain boundary diffusion contributes to the reactive diffusion and the grain growth occurs at certain rates. As the annealing temperature decreases, the contribution of the grain boundary diffusion should become more remarkable, but the grain growth will slow down. Consequently, n becomes close to 1/2 at T = 393 K. According to the constancy of the ratio of the thicknesses, it is concluded that the same rate-controlling process works in the AuSn4, AuSn2 and AuSn layers at a constant annealing temperature.

Kinetics of Reactive Diffusion in Al/Co Multilayers

Kinetics of Reactive Diffusion in Al/Co Multilayers