Irregular growth of AlSb in solid aluminum-solid antimony diffusion couples

An investigation was made of the growth of the intermediate phase aluminum antimonide (AlSb) in solid aluminum-solid antimony diffusion couples, AlSb being the only intermediate phase present in the equilibrum phase diagram. Most diffusion couples were assembled from polycrystalline aluminum and antimony, but a few were made from single crystals; the diffusion couple surfaces were prepared in a variety of ways and the couples were isothermally annealed at temperatures between 450° and 615°C. It was found in all cases that AlSb nucleates at the original interface and after sufficient time coalesces into a highly irregular layer, irrespective of the details of the surface treatment. In several cases in which limited nucleation of AlSb took place, the morphology of the crystals was such as to suggest that the observed anisotropic growth was related to the zinc-blende crystal structure of the AlSb. Formerly Graduate Student, Department of Physical and Engineering Metallurgy, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. Formerly Graduate Student, Department of Physical and Engineering Metallurgy, Polytechnic Institute of Brooklyn.     

Zigzag diffusion paths in multiphase diffusion couples

The diffusion path in a multiphase diffusion couple is predicted to follow a zigzag course when the following conditions are met: the concentration differences between the diffusion couple alloys are small, the alloys contain the same phases, there is one more component in the alloys than the number of phases, and all diffusion takes place in one continuous phase that has a constant diffusivity. An analytical model for the general case of n components and p phases is given that consists of both Heaviside and error functions. The model is consistent with a proposal made by Roper and Whittle concerning “composite diffusion paths” in two-phase ternary systems.     

Pressure effects in multiphase binary diffusion couples

A systematic study has been carried out of the effect of pressure upon growth kinetics of intermediate phases formed in diffusion couples in the binary systems Ni-Al, U-A1, and U-Cu. Even though applied pressures greater than 100 MPa and long times were investigated little or no pressure effect was observed, in disagreement with previous literature reports. The magnitude of observed pressure effects falls within that expected by closure of Kirkendall porosity.     

The early stage of Ni3AI layer growth in NiAI/Ni diffusion couples

The growth kinetics and morphology of the Ni₃Al intermediate phase present in NiAI/Ni diffusion couples have been studied for short times ranging from a few minutes, or less, to a few hours at 1100 °C. Despite high heating rates (<240 seconds to reach 1100 °C), a significant portion of the Ni₃Al layer forms upon heating such that the layer growth which occurs during heating is approximately equal to that which occurs during the first hour of isothermal interdiffusion. TEM studies indicate that the irregular interfaces present at both interphase boundaries are associated with grain boundaries within the Ni₃Al phase. A qualitative model accounting for enhanced layer growth by a grain boundary contribution to diffusion within the Ni₃Al layer is described. formerly with the Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA,.     

Classification of concentration profiles in quaternary diffusion couples

Concentration profiles that can occur in quaternary diffusion couples have been classified into five types according to the number of extrema, the initial concentration differences, and the concentration gradient at the initial interface. The various profiles that are possible have zero, two or four extrema and are illustrated in this work by plotting appropriate error function solutions to the diffusion equation. The conditions under which the different types occur and the transitions between types, are given as well for quaternary systems. The only assumptions made are that the diffusivity is constant in the reaction zone and that the system is single phase.     

Criterion for silicon formation in transition metal-silicon diffusion couples

In this paper, a criterion for silicon formation in metal-silicon diffusion couples, based on the rate of change of free energy, referred to here as the free energy degradation rate (FEDR), has been developed from a kinetic model for silicon formation. In the kinetic model, silicon formation is divided into three steps: diffusion of the predominant diffuser (or moving reactant) to the reactive interface, followed by release of the less mobile species (non-moving reactant) from its lattice and intermixing with the moving reactant, and finally formation and growth of the silicon phase. It has been shown that the free energy change due to silicon formation in a diffusion couple can be determined by examining the free energy change of the reaction region (or reactive interface) located between the growing silicon and the non-moving reactant phase. The free energy degradation rate per unit area of a given reaction region can be expressed as a sum of three contributions, each corresponding to one of the three steps. Each term is a product of a thermodynamic flux and a driving force. These fluxes and driving forces have been examined individually; by analyzing how they change with time, it is shown that when a number of possible reactions compete with one another in a reaction region, there always exists a reaction that will result in the largest FEDR in this region. It is also shown that the largest FEDR leads the system to a relative minimum free energy state that is most stable compared with any other energy state at a given instant.Based on these results, a criterion for silicon reactions has been proposed. During silicon reaction in a reaction region of a metal-Si diffusion couple, there are always a number of possible reactions competing with one another. The reactions which result in the largest FEDR will actually occur. This criterion combined with the new kinetic model has been successfully applied to predict silicon formation in 15 metal-Si systems.     

Microstructural investigation of intermediate phase formation in uranium-aluminum diffusion couples

The irregular growth of the intermediate phase layer which forms as a result of interdiffusion between U and Al has been studied. Using optical and scanning electron microscope examination techniques and electron-probe microanalysis, it has been determined that only one phase (UAl₃) grows in the U-Al system and that the breakdown of interfacial planarity is a result of a limited nucleation rate and rapid growth rate of UA1₃. This phase partially decomposes near the uranium end of the diffusion couple during slow cooling, resulting in the formation of a “multiphase≓ region. No such region is observed in rapidly cooled specimens. X-ray diffraction indicates the absence of a preferential growth direction to the intermediate phase layer. A model is presented that describes the sequence of intermediate phase growth.     

Growth of aluminum antimonide in solid aluminum-liquid antimony diffusion couples

An investigation was made of the isothermal growth of the intermediate alloy phase aluminum antimonide AlSb, at the interfaces of diffusion couples consisting either of solid aluminum and liquid antimony or of solid aluminum and of an Sb−Al alloy slightly supersaturated in AlSb. The diffusion anneals were carried out in the temperature range 635° to 655°C and for times up to 48 hr. In the solid aluminum vs liquid antimony couples, it was found that considerable dissolution of solid aluminum occurred at the solid-liquid interface before the first crystals of AlSb appeared. Subsequently, a two-phase region, consisting of AlSb crystals of greatly varying sizes interspersed throughout the liquid antimony developed between the instantaneous solid-liquid interface and the original solid-liquid interface. The results suggest that the dominant mechanism influencing the growth of AlSb in these diffusion couples is diffusional mass transport of aluminum in liquid antimony. The rapid diffusion of aluminum leads first to the dissolution of solid aluminum and saturation of the liquid antimony, and next to the growth of large discrete crystals of AlSb presumably via an Ostwald-ripening mechanism. N. GRADO, formerly Graduate Student, Department of Physical and Engineering Metallurgy, Polytechnic Institute of Brooklyn, Brooklyn, N.Y.     

Effect of elastic stress on two-phase binary diffusion couples

A front-tracking, finite difference approach has been used to examine the influence of misfit strain and applied stress on interdiffusion in binary, coherent, two-phase planar diffusion couples assuming local thermodynamic equilibrium at the interface. The phases are cubic; possess different lattice parameters, elastic constants, and diffusivities; and can be oriented in either the [001] or [111] direction. Interface compositions, which are time independent in the stress-free case, become time dependent when stresses are present and are affected by both the elastic state of the system and the relative diffusivities. Interfacial compositions can vary by up to a few atomic percent with time and can be either greater or less than the stress-free values for the same set of materials parameters, depending on the volume fraction of the phases. At sufficiently small times, the interfacial position can be approximated as proportional to the square root of time. Interfacial velocities in this regime can differ by up to a factor of 2 from an otherwise equivalent unstressed system. The nonlinear equations resulting from the coupling of stress and composition were linearized in the bulk phases and could be solved either implicitly or explicitly. Equations governing the interface motion and compositions were not linearized and were solved implicitly at each time-step.     

Mass diffusion in polycrystalline copper/electroplated gold planar couples

The Au/Cu system is common to electrical connectors and recent trends toward higher ambient temperatures and thinner gold electroplates focuses attention on a new failure mode. This mode is degradation of thin gold electroplates by mass diffusion of the base metal (copper) to the surface of the electroplate at low temperatures (less than 250°C). Therefore, diffusion experiments were conducted for polycrystalline copper/electroplated gold planar couples over the temperature range of 50° to 750°C. The chemical interdiffusion coefficients, ~D, were calculated using the Boltzmann-Matano solution on the concentration-distance profiles which were determined using an electron microprobe. Results of this study show that ~D is a small function of concentration, generally with a variation of less than a factor of 3 to 5. The correlation of the temperature dependence of ~D between 250° and 750°C with existing data is excellent. The data conform to an Arrhenius equation: ~D= 1.5×10⁻⁵ e^−23,600/RT At temperatures below 250°C the values of ~D deviate from this equation and below 150°C are significantly greater than would be predicted by extrapolating the high temperature Arrhenius equation. No correlation was found between electroplate thickness and diffusion rate.     

The effect of interfacial diffusion barriers on the ignition of self-sustained reactions in metal-metal diffusion couples

An analysis of the solid-state diffusion process leading to exothermic, self-sustained reactions in metal-metal diffusion couples has been performed. Numerical values for the ignition temperature were obtained as a function of interfacial barriers, layer thickness, thermal coupling, and heating rate for isochronal heating of Al-Ni diffusion couples. Of particular interest is the effect of interfacial diffusion barriers, such as oxide layers, on the reaction. These are shown to lead to self-sustained reactions when otherwise not possible and to explain the heating-rate dependence of the ignition temperature observed in experiments. This paper is based on a presentation made in the symposium “Reaction Synthesis of Materials” presented during the TMS Annual Meeting, New Orleans, LA, February 17–21, 1991, under the auspices of the TMS Powder Metallurgy Committee.     

Solid-State diffusion reaction and formation of intermetallic compounds in the nickel-zirconium system

Chemical diffusion studies in the nickel-zirconium system are investigated in the temperature range of 1046 to 1213 K employing diffusion couples of pure nickel and pure zirconium. Electron microprobe and X-ray diffraction studies have been employed to investigate the formation of different compounds and to study their layer growth kinetics in the diffusion zone. It is observed that growth of each phase is controlled by the process of volume diffusion as the layer growth obeys the parabolic law. The activation energies for interdiffusion in NiZr and NiZr₂, which are the dominant phases in the diffusion zone, are 119.0 ±13.4 and 103.0 ±25.0 kJ/ mole, respectively. The formation and stability of compounds over the temperature range have been discussed on the basis of existing thermodynamic and kinetic data.     

Predicting diffusion paths and interface motion in γ/γ + β, Ni-Cr-Al diffusion couples

A simplified model has been developed to predict β recession and diffusion paths in ternary γ/γ + β diffusion couples (γ: fcc, β: NiAl structure). The model was tested by predicting β recession and diffusion paths for four γ/γ + β, Ni-Cr-Al couples annealed for 100 hours at 1200 °C. The model predicted β recession within 20 pct of that measured for each of the couples. The model also predicted shifts in the concentration of the y phase at the γ/γ + β interface within 2 at. pct Al and 6 at. pct Cr of that measured in each of the couples. A qualitative explanation based on simple kinetic and mass balance arguments has been given which demonstrates the necessity for diffusion in the two-phaseregion of certain γ/γ + β, Ni-Cr-Al couples.     

Effect of interfacial kinetic barriers on interface motion in binary diffusion couples

A finite difference scheme is used to examine the effect of misfit strains and interfacial kinetic barriers to the establishment of local thermodynamic equilibrium on the evolution of a coherent interface in a binary diffusion couple. Impediments to the transformation of one phase into the other and to attaining chemical equilibrium at the interface were considered using a matrix of interfacial kinetic coefficients which coupled thermodynamic driving forces with interfacial velocity and fluxes. Interfacial kinetic barriers result in a decrease in the interfacial velocity, a change in temporal power laws, and large shifts in the time-dependent interfacial compositions, sometimes up to 20 at. pct from the time-independent equilibrium values. The interfacial compositions can shift into either the two-phase field or single-phase field depending upon a number of materials parameters, including the initial compositions of the phases comprising the diffusion couple. This article is based on a presentation made in the symposium “Kinetically Determined Particle Shapes and the Dynamics of Solid:Solid Interfaces,” presented at the October 1996 Fall meeting of TMS/ASM in Cincinnati, Ohio, under the auspices of the ASM Phase Transformations Committee.