Vacancy Wind Effect Research Articles

An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple method largely solved the problems. The need to produce two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members may be tricky in certain situations, depending on the complications of diffusion paths. In this study, we have shown the estimation of all types of diffusion coefficients from a single diffusion profile without neglecting Onsager's cross terms in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and concentrated Ni-Co-Fe-Cr-Al quinary alloys. This is applicable in ternary and multicomponent component systems (n≥3) at a stable Kirkendall marker plane position. One can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples following the Hall method, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method proposed in this study will help to generate a mobility database with relative ease in various multicomponent systems important for various applications, which was considered impossible until recently.

Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples

An inventive design strategy of producing the diffusion couples for intersecting the diffusion paths in multicomponent space is described in Ni-Co-Fe-Cr-Al multi-principal element alloy. This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. This was not possible until now following any other experimental methods. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni, and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems. The relative mobilities of the elements are found to follow the trend DNi*≤DCo*<DFe*≤DCr*<DAl* in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is less significant than the intrinsic diffusion coefficients since interdiffusion coefficients are the average of multiple intrinsic diffusion coefficients. This may lead to the wrong statement that the vacancy wind effects are negligible. We have further shown that describing the relative diffusion rates of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Different elements as the dependent variables of interdiffusion coefficients indicate a very different or even opposite trend of relative diffusivities in this system.

Estimation of diffusion coefficients by intersecting different types of diffusion paths in a multi-principal element alloy

A unique method for estimating all types of diffusion coefficients in a multicomponent system is proposed by intersecting only two but different types of diffusion paths. This concept circumvents the limitations of the recently proposed diffusion couple methods, such as pseudo-binary, pseudo-ternary, and the body diagonal method, when practiced individually. Here the diffusion coefficients of all the elements can be estimated as compared to the estimation of diffusivities associated with only two or three elements which develop the diffusion profiles following the pseudo-binary and pseudo-ternary methods, respectively. This also reduces the laborious effort required to bring all the serpentine body diagonal diffusion paths close to each other to estimate the diffusivities with an unknown uncertainty when they do not intersect exactly. On the other hand, as proposed in this study, a serpentine conventional (or body diagonal) diffusion path can be intersected by a rectilinear pseudo-binary diffusion path with relative ease at a specific composition. The modification of the equation schemes for the application of different types of diffusion paths in the estimation of tracer, intrinsic, and interdiffusion coefficients is explained in detail. This method is demonstrated in a model NiCoFeCr multi-principal element system at a composition very close to the equiatomic composition. The influence of the vacancy wind effect on intrinsic and interdiffusion coefficients is described in detail.

Tracer diffusion under a concentration gradient: A pathway for a consistent development of mobility databases in multicomponent alloys

Diffusion in the CoCrFeMnNi high-entropy alloy is investigated using an augmented tracer / interdiffusion couple approach. The tracer diffusion coefficients are measured along the diffusion path developed between the Co17Cr20Fe20Mn20Ni23 and Co23Cr20Fe20Mn20Ni17 end-members allowing an elaboration of a consistent composition-dependent diffusion database. Both tracer and chemical concentration profiles are successfully reproduced to a tolerable level using a pair-diffusion model avoiding the reference element concept. Up-hill diffusion of Co in the experimental profile is not reproduced by the existing kinetic and thermodynamic databases. The reasons for this mismatch are discussed. The calculation of intrinsic and interdiffusion coefficients from the estimated tracer diffusion coefficients utilizing the thermodynamic parameters is demonstrated. The calculated values of the interdiffusion coefficients produced a reasonable match with the interdiffusion flux profiles developed in the multicomponent diffusion couple. The calculation of the vacancy wind effect indicates its strong influence on several intrinsic cross diffusion coefficients.

Correlation between estimated diffusion coefficients from different types of diffusion couples in multicomponent system

The interdiffusion coefficients can be estimated now purely experimentally from multicomponent diffusion profiles utilizing the recently proposed pseudo-binary and pseudo-ternary diffusion couple methods. One can estimate the composition dependent main interdiffusion coefficients over the composition range and main intrinsic diffusion coefficients at the Kirkendall marker plane from pseudo-binary diffusion couple. On the other hand, main and cross interdiffusion coefficients can be calculated from the pseudo-ternary diffusion couples. In this article, we have first proposed the method of estimation of the tracer diffusion coefficients at the cross of diffusion paths in pseudo-ternary diffusion couples by extending the approach propose by Lane and Kirkaldy in a ternary system but without neglecting the cross phenomenological terms of Onsager formalism. Following, one can even estimate the main and cross intrinsic diffusion coefficients, which is otherwise not possible following the Kirkendall marker experiments in this type of couple. Following we have derived the relation for estimation of the tracer diffusion coefficients at the Kirkendall marker plane in a pseudo-binary diffusion couple. We have chosen NiCoFeCr system to demonstrate the utilization of these methods by comparing the tracer diffusion coefficients estimated directly following radiotracer method. The relations derived in this article help to understand the correlation between estimated data in different types of diffusion couples by neglecting and considering the vacancy wind effect. This method can be now extended to the Al, Ga, Si containing systems in which the estimation of tracer diffusion coefficients following the radiotracer method is difficult/impossible because of various reasons.

The Vacancy-Wind Factor and the Manning Factor Occurring in Interdiffusion and Ionic Conductivity in Solids

In crystalline solids, during such processes as chemical interdiffusion in alloys, ionic conductivity and the annealing out of radiation damage there will inevitably be a net flux of vacancies. In most cases, when different species of atoms have different jump rates with vacancies within a net flux of vacancies, the phenomenon of the vacancy-wind effect will occur. This effect was first discovered in the 1960s by the late Dr John Manning. It is a subtle phenomenon that comes about because of the local redistribution of the equilibrium concentration of vacancies with respect to two or more species of drifting atoms in a driving force. The effect is captured in various ‘vacancy-wind factors’ (some of which are now sometimes called Manning factors) which formally arise from non-zero off-diagonal Onsager phenomenological transport coefficients and non-unity values of the tracer correlation factors. In this paper, the effect is reviewed and discussed.

Interdiffusion Studies in β- and γ′-Intermetallic Phases of the Binary Ni-Al System

A critical review of interdiffusion processes in the binary β-NiAl and γ'-Ni3Al intermetallic compounds is presented. The molar volume changes associated with interdiffusion and partial molar volumes of the reacting species, required for the determination of the diffusion parameters, are found using lattice parameter data and, in the case of NiAl, the available information about vacancy concentration within homogeneity range of the β-phase. The presented treatment is purely phenomenological, and its use is convenient since no exlicit assumption of the underlying mechanisms required. A critical analysis of diffusion data for β-NiAl and γ'-Ni3Al ordered phases is followed by discussion of error sources encountered in the interdiffusion experiments. From Kirkendall marker experiments with incremental diffusion couples, information about relative mobilities of species in the intermetallic phases can be obtained, and tracer diffusion coefficients can be deduced using pertinent thermodynamic data on the nickel aluminides. Contribution of the vacancy wind effect to the calculated tracer diffusivities can also be estimated. The Kirkendall plane bifurcation in the Ni41.7Al58.3/Ni72.24Al27.76reaction couple, in which a single-phased layer of β-NiAl intermatallic is formed during interdiffusion from its adjacent phases, is directly related to the growth of grains of the reaction product at a location in between interfaces with starting materials. This diffusion phenomenon can be rationallised using a corresponding Kirkendall velocity diagram. Changes in magnitude and sign of the difference in intrinsic mobilities of the components inside the homogeneity range of the β-NiAl lead to a velocity curve that makes bifurcation of the Kirkendall marker plane possible.

Interdiffusion, Intrinsic Diffusion, Atomic Mobility, and Vacancy Wind Effect in γ(bcc) Uranium-Molybdenum Alloy

U-Mo alloys are being developed as low enrichment uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. In order to understand the fundamental diffusion behavior of this system, solid-to-solid pure U vs Mo diffusion couples were assembled and annealed at 923 K, 973 K, 1073 K, 1173 K, and 1273 K (650 °C, 700 °C, 800 °C, 900 °C, and 1000 °C) for various times. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy and electron probe microanalysis, respectively. As the Mo concentration increased from 2 to 26 at. pct, the interdiffusion coefficient decreased, while the activation energy increased. A Kirkendall marker plane was clearly identified in each diffusion couple and utilized to determine intrinsic diffusion coefficients. Uranium intrinsically diffused 5-10 times faster than Mo. Molar excess Gibbs free energy of U-Mo alloy was applied to calculate the thermodynamic factor using ideal, regular, and subregular solution models. Based on the intrinsic diffusion coefficients and thermodynamic factors, Manning’s formalism was used to calculate the tracer diffusion coefficients, atomic mobilities, and vacancy wind parameters of U and Mo at the marker composition. The tracer diffusion coefficients and atomic mobilities of U were about five times larger than those of Mo, and the vacancy wind effect increased the intrinsic flux of U by approximately 30 pct.

Vacancy wind effect on interdiffusion in a dilute Cu(Sn) solid solution

A study has been conducted on a Cu(Sn) solid solution to examine the role of the vacancy wind effect on interdiffusion. First, the interdiffusion and the intrinsic diffusion coefficients are calculated. The trend of the interdiffusion coefficients is explained with the help of the driving force. Following this, the tracer diffusion coefficients of the species are calculated with and without consideration of the vacancy wind effect. We found that the role of the vacancy wind is negligible on the minor element in a dilute solid solution, which is the faster diffusing species in this system and controls the interdiffusion process. However, consideration of this effect is important to understand the diffusion rate of the major element, which is the slower diffusing species in this system.

Interdiffusion and the vacancy wind effect in Ni–Pt and Co–Pt systems

Abstract

The Nature of the Vacancy-Wind Effect Occurring in Diffusion via Six-Jump-Cycles in B2 Intermetallics

First discovered by the late Dr John Manning, the vacancy-wind effect is a subtle phenomenon that occurs when two or more atomic species compete for vacancies in a net vacancy flux. The vacancy-wind effect is incorporated in (for example) the vacancy-wind or Manning factor that appears in the Darken-Manning Equation relating the interdiffusivity, the tracer diffusivities and the thermodynamic factor. The mechanism of the vacancy-wind phenomenon has long been very poorly understood. Recently, a moving reference frame Monte Carlo method was used to illustrate graphically how the vacancy-wind effect operates in both ionic conductivity in an ionic solid with a dilute solute and chemical interdiffusion in concentrated alloys and ionic compounds. That strategy is extended in this paper to show graphically how the vacancy-wind effect operates in interdiffusion in a stoichiometric intermetallic taking the B2 structure. A simple 4-frequency vacancy diffusion model is used. In previous work, it was shown that depending on composition and temperature, this model can exhibit the six-jump-cycle mechanism. It is shown that in the limit of perfect order that there is no vacancy-wind effect associated with this mechanism when both types of cycle operate equally (zero net vacancy flux). The non-unity value of the vacancy-wind factor found for this mechanism under zero vacancy flux conditions is purely a consequence of a particular geometric mix of tracer and collective atom displacements. The concept that a non-zero off-diagonal phenomenological coefficient provides the vacancy-wind effect is verified.

Visualization of the Vacancy-Wind Effect Occurring in Chemical Diffusion and Ionic Conductivity in Solids

Net fluxes of vacancies commonly occur during chemical interdiffusion in alloys, ionic conductivity and the annealing out of radiation damage. When atoms with different jump rates diffuse in a net flux of vacancies the phenomenon of the vacancy-wind effect will occur. This effect, first discovered by the late Dr John Manning, is a subtle phenomenon arising from a disturbed distribution of vacancies with respect to a given moving atom or species of atom. In this paper, the vacancy-wind effect is discussed and its visualization, performed for the first time by computer simulation, is demonstrated.

Non-Random Interaction of Vacancies with Atoms during Interdiffusion and Ionic Conductivity in Materials

The non-random interaction of vacancies with atoms during interdiffusion and ionic conductivity is referred to as the vacancy-wind effect. This effect, first discovered by the late Dr John Manning, is a subtle phenomenon arising from the non-random distribution of vacancies with respect to a given moving atom within a net flux of vacancies. Recently, a good deal of progress has been made in determining accurate expressions for vacancy-wind factors in binary and ternary alloys, and in mixed cation ionic systems. The present paper provides an overview of these recent findings and puts them into a broader and historical context.

On diffusion in the β-NiAl phase

Interdiffusion coefficients in the β-NiAl phase over the homogeneity range are determined by the diffusion couple technique in the temperature range of 1000–1200 °C. Intrinsic diffusivities of the species at 1000 °C at different compositions are measured by Kirkendall marker experiments. The variations of the molar volume with composition and partial molar volumes of the species, required for the determination of the diffusion parameters, are calculated using lattice parameter and vacancy concentration. Tracer diffusion coefficients of the species were calculated from the knowledge on intrinsic diffusivities and compared with the data available in the literature, which were measured directly by tracer methods. The influence of the vacancy wind effect is determined on the calculated results.

Temperature dependence of vacancy wind effect in β–Zr(Al) solid solution

Temperature dependence of vacancy wind effect in β–Zr(Al) solid solution

The Vacancy Wind Effect in Intermetallic Compounds

The Vacancy Wind Effect in Intermetallic Compounds

The vacancy wind effect for chemical diffusion in intermetallic compounds

Abstract In this paper we examine the behaviour of the vacancy wind factors in the intrinsic diffusivities and the chemical or interdiffusivity in highly ordered stoichiometric AB intermetallic compounds. We show that the six-jump cycle gives quite different limits for these factors from those given by the well-known Manning expressions. Remarkably, there is non-trivial behaviour of these factors even when the vacancy flux is zero. The findings are all verified by computer simulations of a four-frequency model in the square planar lattice and an Ising model in the B2 structure. The consequences of the findings for the interpretation of experimental data are commented on.

The vacancy wind effect for chemical diffusion in intermetallic compounds

In this paper we examine the behaviour of the vacancy wind factors in the intrinsic diffusivities and the chemical or interdiffusivity in highly ordered stoichiometric AB intermetallic compounds. We show that the six-jump cycle gives quite different limits for these factors from those given by the well-known Manning expressions. Remarkably, there is non-trivial behaviour of these factors even when the vacancy flux is zero. The findings are all verified by computer simulations of a four-frequency model in the square planar lattice and an Ising model in the B2 structure. The consequences of the findings for the interpretation of experimental data are commented on.

Darken's equation and other diffusion relations in the light of atomistic kinetic concepts

The atomistic kinetic approach of the DOCC sites concept (meaning, very simplified, that the dopant migration in solids progresses via sites which are suitable for occupation by dopant corpuscles summarized as dopant-occupiable sites, i.e. DOCC sites) is here used as a basis on which several diffusion models are thoroughly analysed. Since it is able to cover all effects determining dopant migrations, so that it may be valid in general, it proves other statements on dopant transport to be incorrectly formulated. Following this conception, Darken's equation leads to a link between the Fickian diffusion coefficient of an ideal solution and the activity coefficient of the non-ideal solution, which has up to now been ignored. Contrasting with Darken's hypothesis, Einstein's relation between the Fickian diffusion coefficient and the mobility of dopant particles proves true even in cases of non-ideal solutions. The supposed vacancy wind effect and the diffusion of dopant-defect pairs as molecule-like joined complexes are shown to be physically unrealistic. Orlowski's dopant flux formula proves false. Roth's and Plummer's model on oxidation-enhanced diffusion in silicon is shown to involve incorrectnesses.

Interdiffusion, intrinsic diffusion and vacancy wind effect in Fe-Al alloys at 1000°C

Diffusion in {beta}(B{sub 2}) and {beta}{prime}(bcc) Fe-Al alloys are of practical interest due to the potential applications at high temperatures. A review of available diffusion data for Fe-rich Fe-Al alloys at 1000 C indicates appreciable differences in the reported values of interdiffusion coefficients. Intrinsic diffusion coefficients and tracer diffusion coefficients are available for selected compositions and temperatures. In this paper are presented interdiffusion and intrinsic diffusion studies carried out at 1000 C with solid-solid diffusion couples assembled with Fe-Al alloys containing up to 50 at.% Al. Intrinsic diffusion coefficients were determined at marker compositions and were employed for an estimation of atomic mobilities and vacancy wind parameters on the basis of a random alloy model incorporating vacancy wind effect. Thermodynamic factors were also assessed at the marker compositions.