Analysis of mean square penetration depth in grain boundary diffusion

Exact and approximate expressions for mean square penetration depth (MSPD) in grain boundary diffusion are derived. The MSPDs in boundary diffusion are functionally different from those in lattice diffusion. The quantitative results obtained provide more reliable estimates for the penetration depth of a diffusant in polycrystalline materials, thin films, and bicrystals.     

Anomalously fast diffusion in the Fe-Zn System

The rate of diffusion of Zn into Fe in solid Fe/Zn diffusion couples is found to be two to four orders of magnitude greater than would be predicted by lattice diffusion. The penetration depth varies markedly from sample to sample. It is achieved primarily in an initial transient, and then stops even though a steep concentration gradient persists in the ferrite. The maximum concentration of Zn in the ferrite surface layer often exceeds the published solubility of the first intermetallic phase, gamma, in ferrite. The initial Zn penetration seems to occur by DIGM. The mechanism for continued penetration is less clear. The variability in percent Zn in the ferrite, and possibly the variation in penetration depth, must stem from the delay in the nucleation of the most iron rich intermetallic phase, gamma. He was a Visiting Scholar at OSU at the time this work was done.     

Diffusion in an ensemble of intersecting grain boundaries forming a triple junction

Grain boundary diffusion in an ensemble of three intersecting grain boundaries forming a triple junction is described in the framework of quasi-steady Fisher’s model. Two configurations, which differ in the number of grain boundaries adjacent to the surface with a diffusant source and in the tilt angle to the surface, are considered. Analytical expressions for the diffusant concentration distribution along each grain boundary that constitutes the triple junction and for the point of the triple junction are derived with the proviso of equal diffusion fluxes at the triple point. The expressions for the diffusant concentration distribution along the grain boundaries include not only diffusion constants (grain-boundary and bulk diffusion coefficients) but also structural characteristics of the ensemble of grain boundaries (the depth of the triple junction point and the angle between the grains forming the triple junction). It is shown that, if the coefficients of grain boundary diffusion are equal for all boundaries making the ensemble and for an equilibrium angle of 120° in a polycrystal, the diffusive mass transport rate in the triple junction zone is lower than that in a single grain boundary irrespective of the configuration of grain boundaries.     

Mössbauer study of the surface barrier to the diffusion of iron into aluminum

A layer of iron was deposited on the surface of an aluminum sample and its diffusion into the aluminum was then studied by means of the Mössbauer effect in⁵⁷Fe. It was found that at high temperature the iron quickly combines with aluminum to form Fe₄Al₁₃, presumably in the form of a thin surface layer. The iron dissolves out of this phase and into the fcc solid solution very slowly at high temperature. This fact helps to account for the holdup of iron at the surface of aluminum as observed in tracer measurements of the diffusion of iron through aluminum.     

The effect of macroscopic solute diffusion in the liquid upon surface macrosegregation

An existing one-dimensional mathematical model that predicts the macrosegregation formation due to solidification shrinkage has been modified to also account for the macroscopic diffusion of solute in the liquid. It is shown both numerically and analytically that such solute diffusion has an almost negligible influence on the predicted solute profile, except in a very thin layer near the chill surface, where severe solute depletion develops. This layer is related to a discontinuity in the diffusive solute flux at the surface, and for a moderately cooled Al-4.5 pct Cu alloy, the layer thickness is of the order 100 μm. When the lever rule is imposed, the solute concentration at the surface becomes equal to the partition coefficient multiplied by the nominal alloy concentration, and the boundary layer solidifies completely once the temperature drops below the liquidus temperature of the (initial) melt. This indicates that assuming local thermodynamical equilibrium at a domain boundary when simultaneously accounting for the macroscale solute diffusion should be reconsidered in macrosegregation modeling.     

Influence of metallic diffusion on the adhesion of screen printed silver films

It is known that the peel strength of a soldered silver thick film will decrease with time of exposure to elevated temperature. The cause of this phenomenon was investigated. Cross sections of thick silver films on dielectric bodies and of the silver film dielectric interface were examined using the electron microprobe. The silver film is bonded to a glass layer, which in turn is bonded to the dielectric body. The bond failure before thermal aging most often occurs at the glass-dielectric interface. After thermal aging, the failure occurs at the silver-glass interface and the magnitude of the peel strength is reduced compared to the former value. In the latter case, the tin from the tin-lead solder was found to have replaced the silver at the silver-glass interface. No lead was found at the interface. The sources of metallic diffusion are considered to be lattice diffusion of the silver into the tin component of the solder, and surface diffusion of the tin over the silver.     

Qualitative observations on the diffusion of copper and gold through a nickel barrier

To retard failure of gold plated copper parts by diffusion of copper to the gold surface, a layer of nickel is frequently used between the copper and gold as a diffusion barrier. To evaluate the mechanisms whereby the nickel retards the motion of copper atoms to the gold surface, planar tri-couples of Cu/Ni/Au were prepared by electroplating nickel and gold layers on OFHC copper coupons. Diffusion anneals were carried out at temperatures from 150 to 750°C. A qualitative evaluation of diffusion behavior was provided by an electron microprobe utilizing X-ray wavelength dispersive analysis on polished cross sections. Results demonstrate that the nickel layer retards but does not block the transport of copper to the gold surface. Possible mechanisms for the anomalous buildup of copper at the gold/nickel interface and gold at the copper/nickel interface are discussed.     

Qualitative observations on the diffusion of copper and gold through a nickel barrier

To retard failure of gold plated copper parts by diffusion of copper to the gold surface, a layer of nickel is frequently used between the copper and gold as a diffusion barrier. To evaluate the mechanisms whereby the nickel retards the motion of copper atoms to the gold surface, planar tri-couples of Cu/Ni/Au were prepared by electroplating nickel and gold layers on OFHC copper coupons. Diffusion anneals were carried out at temperatures from 150 to 750°C. A qualitative evaluation of diffusion behavior was provided by an electron microprobe utilizing X-ray wavelength dispersive analysis on polished cross sections. Results demonstrate that the nickel layer retards but does not block the transport of copper to the gold surface. Possible mechanisms for the anomalous buildup of copper at the gold/nickel interface and gold at thecopper/nickel interface are discussed.     

Room-temperature diffusion in Cu/Ag thin-film couples caused by anodic dissolution

Thin, 100-nm films of first silver and then copper were deposited consecutively onto inert substrates by magnetron sputter deposition. Constant anodic current densities were applied at room temperature to dissolve the outer copper film to varying depths. The 50Cu/50Ag interface, derived from the auger electron spectroscopic concentration-depth profile, initially moved into the copper toward the outer dissolving surface, indicating enhanced diffusion of copper into silver. After longer times at all anodic current densities, the interface reversed and moved back toward the underlying silver-rich layer, indicating that eventually diffusion of silver into copper predominated. The reversal time was inversely proportional to the anodic current density. These effects are explained by anodic formation of subsurface vacancies which migrate as divacancies to the copper/silver interface where they affect interface movements by the well-known Kirkendall mechanism. Calculated diffusivities up to 10⁻¹² cm²/s at maximum anodic current densities of 900 μA/cm² are dramatically above any that are normally observed at room temperature.     

Effect of prealuminizing diffusion treatment on microstructural evolution of high-activity pt-aluminide coatings

The effect of prealuminizing (or prior) diffusion treatment on the evolution of Pt-aluminide coatings on the Ni-based superalloy CM-247 has been studied by using a single-step, high-activity aluminizing process. Coatings generated without any prior diffusion treatment, as well as those formed by adopting two extreme prior-diffusion schedules (at 850 °C for 0.5 hours and at 1034 °C for 5 hours), were investigated by analyzing the coating structures at various stages of aluminizing. When the dilution of the Pt layer, caused by its interdiffusion with the substrate during the prior diffusion treatment, is only marginal (as in the case of no prior diffusion and diffusion at 850 °C for 0.5 hours), the equilibrium Pt-aluminide coating structure evolves through the formation of two transient layers during the initial stages of aluminizing. In contrast, for diffusion at 1034 °C for 5 hours, which results in extensive dilution of the Pt layer, the two-phase equilibrium structure (PtAl₂ in a matrix of NiAl) in the outer layer of the coating is found to develop during very early stages of aluminizing and remains unchanged, even over extended periods of aluminizing. Further, in the case of prior diffusion at 1034 °C for 5 hours, Pt is found to remain distributed to a greater extent over the entire thickness of the coating than in the cases of limited prior diffusion treatment. The present findings underline the significance of the nature of the prior-diffusion schedule on the microstructural evolution of Pt-aluminide coatings. It has also been found that a prealuminizing diffusion treatment is particularly important for Pt-aluminide coatings from the point of view of coating adhesion to the substrate.     

Room-temperature diffusion in Cu/Ag thin-film couples caused by anodic dissolution

Thin, 100-nm films of first silver and then copper were deposited consecutively onto inert substrates by magnetron sputter deposition. Constant anodic current densities were applied at room temperature to dissolve the outer copper film to varying depths. The 50Cu/50Ag interface, derived from the auger electron spectroscopic concentration-depth profile, initially moved into the copper toward the outer dissolving surface, indicating enhanced diffusion of copper into silver. After longer times at all anodic current densities, the interface reversed and moved back toward the underlying silver-rich layer, indicating that eventually diffusion of silver into copper predominated. The reversal time was inversely proportional to the anodic current density. These effects are explained by anodic formation of subsurface vacancies which migrate as divacancies to the copper/silver interface where they affect interface movements by the well-known Kirkendall mechanism. Calculated diffusivities up to 10⁻¹² cm²/s at maximum anodic current densities of 900 μA/cm² are dramatically above any that are normally observed at room temperature.     

Kinetics of diffusion in the Nb-Al system

Diffusion kinetics were studied by varying the time and temperature (800° to 1300°C) of dipping solid niobium into molten aluminum. It was found by X-ray diffraction analysis that only the Al₃Nb phase forms at the surface of the niobium specimen and that the thickness of this layer for a given dip temperature varies parabolically with time. The activation energy and the preexponential factor of the diffusion parameter, (δD) were found to be 36.5 ∓ 0.45 kcal per mole and 2.0 ∓ 0.34 sq cm per sec, respectively.     

Quasi-static intergranular brittle fracture at 0.5 tm: A non-equilibrium segregation mechanism of sulphur embrittlement in stress-relief cracking of low-alloy steels

A theory of elastic-plastic-diffusive crack growth along grain boundaries is developed and compared with experimental observations of stress-relief cracking of low-alloy steels. Intergranular decohesion advances atomistically by coupled surface and grain-boundary diffusion, while the macroscopic plain-strain crack grows quasi-statistically by maintaining a deformation field in small-scale yielding. Near an advancing crack tip, a surface diffusion distance is found within which steady-state diffusion is driven by a sharp curvature, while a corresponding boundary diffusion distance is found within which diffusion plating overtakes elastic-plastic stretching to smooth out the stress concentration. Diffusional and elastic-plastic processes at an extending crack tip are thus coupled to each other and to the loading parameter at distance. Fast diffusants are predicted to accumulate near the crack tip on both surfaces and grain boundary, confirming a recent scanning Auger observation of sulphur segregation by Hippsley et al. Considerations of non-equilibrium interfacial energies and fracture work reveal the embrittling role of sulphur, both as a fast diffusant and as a strong surface segregant. Predictions of growth rates are in excellent agreement with the data of Shin and McMahon, over the entire range of stress intensity factor and temperature studied. Metallurgical factors promoting brittle stress-relief cracking in the heat-affected zones of welding of low-alloy steels, including sulfide distribution, hot yield strength, and notch sensitivity, are explained.     

The Effect of Pressure Modulation on the Flow of Gas through a Solid Membrane: Permeation and Diffusion of Hydrogen through Nickel

The attenuation and phase lag of pressure modulations transmitted through a solid foil from one chamber to another may be used to assess the diffusion and solubility coefficients of diffusant gas in the solid. A linear approximation is used to describe the cases of flow into (1) pumped and (2) equilibrated output chambers. It is shown that experiments based on this kind of system allow self-consistency checks to confirm diffusion limited flow and that pumped systems allow direct estimation of the index of the power law describing permeation. Experiments with hydrogen in nickel using a pumped system demonstrate close adherence, over a wide range of experimental parameters, to the expected frequency variation of output. Formerly with The Open University, Oxford, United Kingdom     

Lithium diffusion in aluminum-lithium alloy 2090 clad with 7072

The loss of lithium during solution heat treatment of alloy 2090 clad with approximately 100 μm of 7072 was investigated. Lithium concentration profiles in the alloy were measured using a nuclear reaction analysis technique after samples had been subjected to various solution heat treatments. The results showed that the cladding-base metal interface provided no impediment to lithium diffusion and that the rate of lithium diffusion in the cladding was similar to its rate of diffusion in the base metal. A lithium-rich oxide was formed on the external surface, but the concentration profiles showed that the effective lithium concentration at the surface was near zero. Thus, lithium in the bulk experienced a maximum concentration gradient and diffused to the surface as rapidly as possible. Despite the absence of any lithium diffusion barrier in the cladding, the initial rate of lithium loss is much less than in bare material. The cladding provides effective protection from lithium loss, and the rate of loss in clad materials only approaches that of bare materials after approximately 4 hours.     

Composition and properties of the diffusion layer formed upon heat treatment of an aluminum gas-thermal coating on titanium

An aluminum gas-thermal coating 200–300 μm thick is deposited onto the surface of titanium samples with an arc discharge. After heat treatment of the samples at 900 or 1000°C for 2, 4, or 6 h, the chemical composition and properties of the diffusion layer formed as a result of titanium and aluminum interdiffusion are studied. The main phase of the diffusion layer is found to be TiAl₃. The fractions of the phases TiAl₂, TiAl, and Ti₃Al are insignificant. The adhesion of the diffusion layer to the titanium substrate, the wear resistance, the friction coefficient, the hardness, the corrosion resistance, and the thermal and electrical conductivities are studied as functions of the heat-treatment temperature and time.     

The effect of pressure modulation on the flow of gas through a solid membrane: Surface inhibition and internal traps

By permeation of a gaseous diffusant, pressure modulations may be transmitted through a solid foil from one experimental chamber to another. The resulting attenuation and phase lag of the transmitted modulation depend on all processes capable of influencing the diffusant flux. It is shown that diffusants which take part in surface reactions of finite rate or are subject to reversible trapping within the solid have a frequency response characteristic of the process involved. Mathematical separation of the bulk and surface processes is effected by a treatment which uses a separate matrix to describe each process and so is readily applied to the problem of multiply controlled flows. The analysis suggests that experimental separation of processes is possible even when both surface reaction and internal trapping have a part in determining rate of flow.     

Boundary conditions for the diffusion equation in radiative transfer

Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach.     

The solvent-fixed coordinate system applied to two-phase diffusion coatings resulting from a constant surface flux of solute

The explicit finite difference form of the diffusion equation has been used to describe a two-phase binary diffusion problem which includes a constant surface flux boundary condition, a concentration-dependent diffusion coefficient, and dimensional change due to both additions of material and nonideal solution behavior. The ξ_γ coordinate system, containing an equal number of mols of the substrate component per increment, has been employed to simplify the mathematical form of the diffusion equation. At the two-phase interface a Lagrangian extrapolation has been employed in conjunction with the finite difference equations to determine solute concentration and flux as well as interface movement. Results of sample calculations for the α and β phases formed when a constant flux of aluminum is admitted to a copper surface at 850°C are presented graphically. Results include concentration profiles, surface concentration as a function of time, and movement of theα-β interface for a flat plate and for a cylinder. This treatment is applicable to any two-phase binary system wherein the arrival rate of solute atoms at the solvent surface, either by ionic transport in high-temperature electrodiffusion cells or from the vapor phase, is equal to the diffusion rate into the surface.     

A coupled diffusion model for the reduction of agglomerates of iron oxide granules

A coupled diffusion model is presented to describe the reduction of agglomerates of ferrous oxide grains. The reducing gas (CO) is imagined as diffusing first through the boundary layer created by gas flow at the pellet surface, then through, the agglomerate and finally diffusing into individual grains toward a moving boundary where the reduction occurs. The model is a general one applicable to packed beds of ore particles, briqueties or with some simplication to spherical pellets. Analytic solutions are obtained for platelet grains in slabs and the reduction of spherical pellets of spherical grains is computed for a range of values of the ratio of diffusivities of CO in the grains and pellet.