High Diffusivity Paths Research Articles

Oxygen self-diffusion along high diffusivity paths in forsterite.

Diffusion profiles of 18O tracer in single crystals of forsterite following anneals at 1100° and 1200°C have been determined by a depth profiling technique using secondary ion mass spectrometry. The diffusion penetration profiles showed error function forms with developed tails. The profiles were analyzed in terms of diffusion in the forsterite lattice together with a contribution from dislocation. The present results of lattice diffusion lie in the range of the extrapolation of lines on Arrhenius plots reported previously for intracrystalline diffusion in forsterite. The dislocation diffusion coefficients are about 104 times faster than the lattice diffusion at the same temperature. Diffusion along the dislocations takes place within a pipe with radius of about 0.1 nm surrounding the dislocation line. Based on the above results, O diffusion along high diffusivity paths, such as dislocations and grain boundaries, play an important role on the diffusional creep in olivine under laboratory condition.

SiCウィスカー強化6061アルミニウム合金複合材料の時効析出挙動

The majority of existing models which predict mechanical properties of composites assume that matrix properties are unchanged by presence of reinforcement. However, preliminary investigations have shown that there are never negligible effects of the reinforcement on the matrix microstructure. For example, accelerated aging of the composite has been reported recently. The objective of this article is to document the effects of the reinforcement on the aging response of the cast 6061 aluminum matrix.Cast reinforced composites containing 22% volume fraction of silicon carbide whisker were fabricated by high pressure infiltration technique. The age-hardening behavior of the 6061 aluminum alloy with and without SiC whisker was studied using hardness measurement, calorimetric technique and transmission electron microscopy.The over-all age-hardening sequence is not altered by the addition of SiC whisker. Moreover, the maximum hardness of 6061 with and without SiC whisker is associated with the same transition stage from the GP(II) zone to the intermediate β′ phase. However, precipitation kinetics of the matrix alloy is affected by presence of the reinforcement. Times to achieve the peak hardness are shortened in the composites over the whole temperature ranges investigated. But this tendency becomes remarkable with low aging temperature, suggesting the contribution from high diffusivity paths such as dislocations and reinforcement-matrix interfaces. This acceleration is attributed to the drastic decrease of the activation energy required for the formation of the GP(II) zone and intermediate β′ phase. In contrast, the GP(I) zone formation is slightly retarded by the whisker. Furthermore the fraction transformed data were fitted to the Johnson-Mehl-Avrami type time dependence expressions and reaction rate order, n, is obtained as a function of temperature. The data explain a role of dislocations as precipitation sites. Finally microscopic observation was performed to confirm the above-mentioned experimental results.

Core Level Orbital Interactions and Fast Ion Conduction

AbstractAlthough there has been much success in theoretical modelling of fast ion conductors with molecular dynamics simulations, there has been less attention paid to development of a chemical understanding of fast ion conduction. In this paper we explore the importance of core level interactions and the role that they play in constructing high diffusivity paths in solids. In particular, we have carried out molecular orbital calculations (using the self-consistent-field X-alpha scattered-wave method) on AgI clusters to examine the orbital interactions of the filled Ag 4d level. We hypothesize that it is the interaction of the d electrons that is responsible for fast ion conduction in AgI and other Ag and Cu binary fast ion conductors. The results of these calculations will be compared with other electronic structure calculations and XPS data.

Compositional changes of minerals associated with dynamic recrystallizatin

The rate of compositional and isotopic exchange between minerals may be enhanced significantly if the rock is deformed simultaneously. The enhanced exchange rate may result from a reduction in grain size (shorter distance for volume diffusion), dissolution and growth of grains by diffusion creep (pressure solution), or the movement of high-angle grain boundaries through strained grains during recrystallization in the dislocation creep regime. The migration of high-angle grain boundaries provides high diffusivity paths for the rapid exchange of components during recrystallization. The operation of the latter process has been demonstrated by deforming aggregates consisting of two plagioclases (An1 and An79) at 900°C, 1 GPa confining pressure, and a strain rate of ∼2x10-6s-1. The polygonal, recrystallized grains were analyzed using an analytical transmission electron microscope and have a variable but often intermediate composition. At the conditions of these experiments, the volume interdiffusion rate of NaSi/CaAl is too slow to produce any observable chemical change, and microstructural-chemical relations indicate that the contribution from diffusion creep was insignificant except for initially fine-grained (2–10 μm) aggregates. These results indicate that strain-induced recrystallization can be an effective mechanism for enhancing the kinetics of metamorphic reactions and for resetting the isotope systematics of minerals such as feldspars, pyroxenes, and amphiboles.

Experimental studies of grain boundary diffusion of hydrogen in metals

Electrochemical permeation tests and silver decoration tests were performed in polycrystalline nickle with different grain sizes. Comparison of experimental results with theoretical predictions of a newly proposed grain boundary diffusion model indicates that grain boundaries are not high diffusivity paths for hydrogen. The sominant role played by grain boundaries during mass transport of hydrogen is retardation due to the trapping effect. The grain boundary diffusivity of hydrogen is concentration dependent. When the hydrogen concentration is extremely low, the grain boundary diffusion of hydrogen is virtually stopped. It is postulated that the low energy sites within grain boundaries are responsible for such retardation.

Elevated temperature microstructural stability of Al +-ion implanted nickel

Composition profiles were measured following 180 keV Al +-ion implantation of nickel at temperatures up to 600°C, and following 600°C annealing of nickel implanted at 25°C. The phases present in the implanted layers were identified and are compared to those found on the NiAl phase diagram. The implanted compositions are nearly temperature independent at fluences below 1.5 × 10 18 ions/cm 2. The Al concentration reaches 70 at.% Al by 3 x 10 18 ions/cm 2 fluence delivered at 25°C, and it extends to 3000Å depth. Beyond 1.5 × 10 18 ions/cm 2 fluence delivered at 500°C, an Al composition of 25% extends to 6000Å depth, well beyond the ~ 100Å increase in depth due to radiation-enhanced diffusion. Similar results obtain for 25°C implanted specimens subsequently annealed at 600°C. TEM examination shows the defect-enriched region beyond 3000Å recrystallizes at elevated temperatures and enhances diffusion via the high diffusivity paths provided by the grain boundaries. Phases found in elevated temperature specimens often differ from those in 25°C implanted specimens. Comparing the former with the latter: Ni 3Al replaces the extended portion of the Al in Ni f.c.c. solution; Ni 3Al and NiAl replace an h.c.p. phase peculiar to lower temperatures; and phases richer than 50% Al are replaced by Ni 3Al due to compositional instabilities. Phase prediction based on local chemical composition and the phase diagram is shown to be valid, but can proceed only when the compositional instabilities are taken into account.

The influence of alloy diffusion processes on the corrosion of ferritic and austenitic stainless steels

Sulphidation has been studied in austenitic steels AISI 310 and 447 and in ferritic steel AISI 446 at temperatures between 550°C and 700°C. The kinetics of mass gain change at about 650°C from a linear, spalling-controlled type at lower temperatures to a diffusion-controlled type above this temperature. At the higher temperatures internal sulphidation is observed. The explanation for the mass gain rate constants measured is that diffusion in the alloy is rate controlling. This is substantiated by a new high diffusivity-path-enhanced diffusion model described in a parallel paper. The high diffusivity paths are shown to be intergranular and intragranular sulphides, in ferritic and austenitic alloys, respectively. These sulphides nucleate on existing carbides. In cases where the aggressiveness of the atmosphere is not high, as is the case here, this alloy diffusion controlled corrosion mechanism can be suppressed by using austenitic as opposed to ferritic matrices and reducing the concentration of relatively unstable carbides like M 23C 6 in the material.

“Pressure solution” creep: Some causes and mechanisms

Despite the widespread evidence of stress‐controlled dissolution and precipitation in diagenetically altered and low‐grade metamorphic rocks, a great deal of controversy remains concerning the driving forces and transport mechanisms involved. To clarify the various driving forces, the free enthalpy equation is expanded here to allow identification of different terms contributing to the overall phenomenon. It is argued that under diagenetic conditions, stress concentrations at grain‐to‐grain contacts will be the largest source of chemical potential gradients and that upon burial and cementation these inhomogeneities decline and the orientation dependence of normal stress in a quasi‐homogeneous stress field becomes important as well. These mechanisms operate efficiently enough under these relatively cold, H2O‐rich conditions that stresses can remain below the threshold for crystal plastic deformation. Water on grain boundaries provides at the very least a high diffusivity path and in cases of large volume losses must also contribute directly through fluid flow. Most experimental work on this phenomenon has not distinguished carefully between stress‐enhanced solubility and solubility enhancement due to plastic deformation or microcracking. A new thermodynamic analysis of the results of some experiments by Sprunt and Nur suggests that in at least some of their experiments, true pressure solution creep has been activated. A related phenomenon, volume transfer creep during phase transformations which involve significant volume change, displays many of the characteristics of pressure solution.

AES studies of palladium films formed on copper and mica

Thin epitaxial films of palladium were grown on epitaxial copper films and cleaved mica in ultra high vacuum. The growth modes of these films were investigated by Auger electron spectroscopy (AES), low energy electron diffraction (LEED), transmission electron microscopy (TEM), and TEM replica techniques. Layer by layer growth of Pd on Cu and mica was observed and inelastic mean free paths of Auger electrons for energies of 60 eV (Cu MMM) and 329 eV (Pd MNN) were calculated. These values were 5.7 and 6.9 Å respectively. The thermal stability of monocrystalline and polycrystalline Pd/Cu bilayer films at 483 K was also investigated by AES and TEM. It was found that Pd agglomerates on the Cu at this temperature to form a Stranski-Krastanov growth morphology. The agglomeration is much more rapid on polycrystalline films, suggesting that high surface diffusivity paths (grain boundaries and possibly other defects) enhance the surface diffusion of Pd on Cu.

Aes studies of palladium films formed on copper and mica

Thin epitaxial films of palladium were grown on epitaxial copper films and cleaved mica in ultra high vacuum. The growth modes of these films were investigated by Auger electron spectroscopy (AES), low energy electron diffraction (LEED), transmission electron microscopy (TEM), and TEM replica techniques. Layer by layer growth of Pd on Cu and mica was observed and inelastic mean free paths of Auger electrons for energies of 60 eV (Cu MMM) and 329 eV (Pd MNN) were calculated. These values were 5.7 and 6.9 Å respectively. The thermal stability of monocrystalline and polycrystalline Pd/Cu bilayer films at 483 K was also investigated by AES and TEM. It was found that Pd agglomerates on the Cu at this temperature to form a Stranski-Krastanov growth morphology. The agglomeration is much more rapid on polycrystalline films, suggesting that high surface diffusivity paths (grain boundaries and possibly other defects) enhance the surface diffusion of Pd on Cu.

Gigaohm-range polycrystalline silicon resistors for microelectronic applications

The objective of this work was to investigate the conduction properties of very high resistance devices formed from undoped chemical-vapor-deposited polycrystalline silicon. Test structures having resistances as high as 600 GΩ at 5 V were fabricated, of a size suitable for microelectronic device applications. Detailed measurements of current-voltage characteristics in the dark and with photoexcitation, the effect of resistor length, and the temperature dependence of resistance, were made. The data is interpreted in terms of a model based on avalanche breakdown of the reverse-biased n+-i junction, with the current limited by the remaining quasi-neutral i-region. Theoretical current-voltage curves and the dependence of effective resistance on device length are calculated with the model, showing all the qualitative aspects of the data. Incorporation of gigaohm-range load resistors into a 16K CMOS static RAM cell is described. The work shows the dominant effects of grain boundaries in controlling current transport in undoped polysilicon, providing high-diffusivity paths for impurity diffusion, and apparently determining the reverse breakdown behavior of the junctions present.

A random walk model for diffusion in the presence of high-diffusivity paths

Abstract Diffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. In porous media such as rocks, fissures provide a system of high-flow paths. Recently, based on a continuum approach, these phenomena have been modelled, resulting in coupled systems of partial differential equations of parabolic type for the concentrations in the bulk and in the high-diffusivity paths. This theory assumes that each point of the media is simultaneously occupied by more than one diffusion or flow path. Here a simple discrete random walk model of diffusion in a media with double diffusivity is given. The continuous version of this model gives rise to precisely the coupled system of partial differential equations obtained from the continuum approach. For the discrete model the problem of the unrestricted particle is considered. This problem corresponds to the source solutions of the continuous model and an approximate asymptotic expression is deduced from the random walk model for the total concentration. This expression illustrates clearly the departures from classical findings due to the high-diffusivity paths.

An integral equation arising in double diffusion theory

Diffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. Diffusion in a media with two distinct families of diffusion paths is modelled by two coupled linear partial differential equations of parabolic type with diffusivities D 1 and D 2. Physically the situation D 2 ⪡ D 1 is of some considerable interest and previously established results, for D 2 non-zero, for the solution of boundary value problems, are not applicable to the idealized theory characterized by D 2 vanishing. An integral equation, which arises in the solution of boundary value problems for this idealized theory, is formally solved.

A discrete random walk model for diffusion in media with double diffusivity

AbstractDiffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals, high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. In pourous media such as rocks, fissures provide a system of high-flow paths. Recently, based on a continuum approach, these phenomena have been modelled, resulting in coupled systems of partial differential equations of parabolic type for the concentrations in bulk and in the high-diffusivity paths. This theory assumes that each point of the medium is simultaneously occupied by more than one diffusion or flow path. Here a simple discrete random walk model of diffusion in a medium with double diffusivity is given.

Some theoretical aspects of diffusion in the presence of high-diffusivity paths

In metals high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. Recently Aifantis [1,2] has proposed a continuum theory modelling diffusion of ions and point defects in the presence of high-diffusivity paths. This theory assumes that each point of the media is simultaneously occupied by N diffusion paths and a coupled system of N partial differential equations of parabolic type are obtained for the concentrations ci(x,t) (i = 1,2 ..... N) in each diffusion path. The purpose of this note is to present a simple discrete random walk model which in the continuous limit gives rise to precisely this coupled system of partial differential-equations. This formulation gives the signs of various constants appearing in the theory which were previously based on ad-hoc physical arguments. Moreover for source solutions an approximate expression for the total concentration can be deduced from the discrete model. This expression illustrates clearly departures from classical findings due to the high-diffusivity paths.

Diffusion induced grain boundary migration

While grain boundaries and interphase boundaries provide high diffusivity paths in solids, little bulk composition change can occur at temperatures where lattice diffusion is frozen out unless the boundaries migrate. That the diffusion itself can induce boundary migration has been suspected for some time. This study reviews evidence that the effect is indeed common, and this conclusion is reinforced by additional observations on three systems. (GHT)

A new interpretation of diffusion in high-diffusivity paths—a continuum approach

We consider the problem of diffusion in regions containing a finite number of continuously distributed families of high-diffusivity paths. We assume linear diffusion processes and we provide differential expressions for the partial and total concentrations. The basic equations are specialized to study in detail diffusion in media with a single family of high-diffusivity paths. In this case we derive a system of two simultaneous second-order linear differential equations for the concentrations at the regular and high-diffusivity paths. Uncoupling of the equations yields a fourth-order linear differential equation for the total concentration. The various differential equations show the coupling of the partial diffusion processes and the non-Fickean character of the total diffusion process. Certain steady and non-steady boundary-value problems are formulated and solved to illustrate the departure of our findings from the classical interpretations.

Continuum basis for diffusion in regions with multiple diffusivity

A continuum model is proposed to consider diffusion situations where distinct types of structural or point defects contribute to the overall diffusivity. With respect to structural defects, the analysis is motivated by diffusion in the presence of a continuous distribution of high-diffusivity paths, such as grain boundaries and dislocations. With respect to point defects, the analysis is motivated by simultaneous diffusion of vacancies and interstitials, or vacancies and substitutionals. As a result of continuum modeling, the analysis is strictly valid in cases where the distribution of defects can be assumed continuous in space-time. The model is illustrated by detailing an example: dislocation-pipe diffusion under steady-state conditions.

Interdiffusion in the Co-Ni system-I concentration penetration curves and interdiffusion coefficients

The interdiffusion in the Co-Ni system has been investigated in the temperature range of 950 to 1150 °C, by means of diffusion specimens of pure Co and Ni. The concentration curvesN(x, t) obtained with the aid of an JXA-3 A JEOL electron microprobe were evaluated using the smoothing cubic spline method by means of the Boltzmann-Matano equation. The obtained interdififusion coefficient values ¯D increase with the increasing Ni concentration and satisfy the Arrhenius equation at temperaturesH ≧ 990 °C. At lower temperatures the influence of high diffusivity paths may be effective, resulting in higher ¯D values. No expressive influence of atomic (Ni3Co) or magnetic order on the interdiffusion has been detected. The activation enthalpyΔH values were found almost concentration independent. A Kirkendall effect study has been carried out with positive results which are presented in Part II of this paper. A new method for the determination of diffusants concentration in the Kirkendall plane was proposed. With the use of this method and of Darken equations the intrinsic diffusion coefficients were calculated. These results are given in Part III.

Atomic diffusion in alloys exposed to liquid sodium

Abstract Reasons for the observed enhancement of atomic diffusion coefficient in alloys exposed to sodium are explored. The diffusion coefficient in the presence of a chemical potential gradient is derived from a simple atomistic model. It is concluded that two mechanisms could contribute to the enhancement, (a) A non-zero gradient of partial molar enthalpy, (b) An increase in the atomic mobility due to the presence of high diffusivity paths. It is shown that the effect of (a) is not of sufficient magnitude to account for the increase in coefficient. However the results can be analysed successfully in terms of grain boundary diffusion and the coefficients are determined for iron in Ni/Cr (1.2 × 10 −9 cm 2 /s) at 650°C and nickel in iron (5 × 10 −8 cm 2 /s) at 730°C. The total absorbed diffusant is also calculated for the case of iron into Ni/Cr, and a general expression for the absorbed diffusant is given.