Concentration-penetration Curves Research Articles

Short circuit diffusion in CuSn6/Ni/Au planar tricouples

To investigate processes of short circuit and uphill diffusion, low-temperature diffusion experiments were carried out with sandwich samples of CuSn6/Ni/Au in the kinetic regimeB after Harrison. Two kinds of base material CuSn6 with different grain sizes were chosen. The first material was cold rolled CuSn6 with a mean grain size of 3–4 μm. The second was annealed CuSn6 with a mean grain size of 40 μm. The Ni and Au layers with thicknesses in the μm range were deposited by galvanization. The sheets were prepared by ion beam slope cutting, characterized by scanning electron microscopy and transmission electron microscopy. After annealing at 576 K up to 120 d, the samples were investigated with glow discharge spectroscopy and scanning electron microscopy. Concentration penetration plots made with glow discharge spectroscopy showed a different diffusion behaviour dependent on the CuSn6 material. The diffusion processes in the samples of cold rolled CuSn6 are more extensive than in the annealed CuSn6 samples. To find out causes of this phenomenon, a model of short circuit diffusion was developed and concentration penetration curves were calculated numerically with the finite difference method. Images of an ion beam slope cut sample show grain growth in the Au layer.

The Kirkendall effect of the Al-Cu couple with an electric field

In their well known experiment, Smigelskas and Kirkendall [1] demonstrated that an imbalance of intrinsic fluxes, the Kirkendall effect, leads to porosity and the displacement of markers located in the reaction zone of a diffusion couple. Marker movement normally occurs in binary diffusion couples because the sum of two intrinsic fluxes is generally finite. However, if the marker velocity is controlled, the intrinsic fluxes might sum to zero at the marker plane so that there is a negligible Kirkendall effect. The study of the Kirkendall effect of the Al-Cu couple [2] indicates that the marker leaves the interface to move towards the aluminium side of the Al-Cu couple because the aluminium diffuses more rapidly than does the copper. In order to reduce or eliminate marker movement and porosity, the Kirkendall effect of the Al-Cu couple with an electric field was investigated. In the study, diffusion couples of pure Al (99.99%) and oxygen-free Cu (99.99%) were used. Molybdenum wire was used as a marker to measure the Kirkendall effect with the aim of discussing marker movement with an electric field. Fig. 1 shows a schematic drawing of the electric field. The Al-Cu couples were heated at 530 1 8C for 8 h in electric field strengths of 1, 2 and 4 kV=cm). The marker displacements and the intermediate phases in the different conditions were observed by electron probe microanalysis (EPMA). The concentration-penetration curves were also established using EPMA. As shown in Fig. 2, the marker displacements are observed by a scanning electron microscope (SEM). With no electric field, the marker leaves the interface to move towards the aluminium side of Al-Cu couple. However, with an electric field (E ˆ 4 kV=cm), the marker moves towards the copper side of the Al-Cu couple. This implies that the electric field inhibits the Kirkendall effect. Fig. 3 shows the displacements of marker movement in the different electric field strengths. With increasing electric field the displacement of the marker is reduced compared to that with no electric field. The displacements of the marker depend approximately linearly on the electric field strengths. As shown in Fig. 4, intermediate phases are observed in the diffusion zone of the Al-Cu couple by EPMA. The same intermediate phases are observed in the various treatments. With increasing electric field strength, the c2, ae2, a and a2 phases are inhibited, but the Ł phase is promoted, which indicates that the electric field treatment accelerates the diffusion of copper atoms but retards the

Diffusion, the Kirkendall effect and vacancy jump frequency ratios in dilute Al-Zn alloys

The method of vapour-solid couples was applied in order to investigate interdiffusion and intrinsic diffusion in dilute Al-Zn alloys. Although an aluminium oxide layer could not be avoided in our experiments, typical concentration-penetration curves were measured by electron probe microanalysis. The Boltzmann-Matano evaluation of the profiles yielded interdiffusion coefficients in agreement with previously published results. Contrary to the expected behaviour, bulges were observed by metallographic inspection at those regions of surfaces where zinc diffused into the samples. From results of interdiffusion and from measurements with only 1h diffusion time, it is deduced that the penetration of Zn atoms is nearly unaffected by the surface oxide layer and shows no local differences. Therefore, the reason for the growth of the bulges is the diffusion of the host component Al, which is possible only at preferred sites of the oxide layer. The ratio DZn/DAI was determined at those sites where the oxide layer was penetrated by both Zn and Al atoms. From the value measured for an infinitely dilute solution, (DZn/Dl))0=1.70+or-0.25, the vacancy flow factor (LAlZn/ZnZn)0=-0.19+or-0.13 was derived. Vacancy jump frequency ratios according to the five-frequency model were calculated which differ from unity only slightly and are similar to those obtained for the systems Ag-Zn and Cu-Zn. A weak binding between vacancies and Zn impurity atoms was estimated by means of two different methods.

A practical solution for the diffusion equations in binary and multicomponent systems with constant intrinsic diffusion coefficients

A practical solution for the diffusion equations in binary and ternary systems is presented which leads to a prediction of the concentration-penetration curves, diffusion paths, and the values for the intrinsic and interdiffusion fluxes. The model is very simple and gives insight into a variety of diffusion phenomena and zero-flux planes. The model has been applied to systems in which the intrinsic diffusion coefficients are constant and which, as far as ternary systems are concerned, are thermodynamically ideal. Although not mathematically exact, the results agree within the expected experimental accuracy with exact solutions presented in the literature. Even if the intrinsic diffusion coefficients are not constant, or if the ternary system is not thermodynamically ideal, the results agree semi-quantitatively with experimental results found in the literature. With some adaptations the agreement will be still better.

Ternary Diffusion. Solutions with Diffusion Coefficients Linearly Dependent on Concentrations

A numerical solution was devised for the set of differential equations characterizing interdiffusion in a ternary system in which the partial diffusion coefficients are linear functions of the concentrations. A one-step fourth order Runge-Kutta method was used in the computer program. The concentration-penetration curves obtained accurately reflect the behavior of an interdiffusing ternary ideal solid solution provided that the tracer diffusion coefficients are constant and the ratios of the latter are not very different from unity. A theorem was derived which specifies the conditions for which the points of inflection of the three concentration-penetration curves occur at the same position in the diffusion couple. Also, it was shown that in an ideal interdiffusing ternary solid solution, zero-flux plane positions cannot correspond exactly to the points of intersection of the diffusion path and iso-activity lines drawn through the terminal alloys of the diffusion couple, but approach the latter in the limiting case. Finally, a method was developed to calculate the partial interdiffusion coefficients at a composition point on the diffusion path of an ideal ternary solid solution diffusion couple through the use of information obtained only from that one diffusion couple.

Impurity diffusion of Ni in Co 1− xO single crystals

Nickel diffusion coefficients have been measured in cobalt oxide Co 1− x O, under oxygen partial pressures of 0.21 atm and 1.5×10 −5 atm in a large temperature range (1000–1600°C). NiO has been deposited as a thin film on the surface of CoO single crystals by rf sputtering. Concentration-penetration curves have been obtained by electron beam microanalysis and by secondary ion mass spectrometry. The results can be described by the relations: D CoO Ni (cm 2/s) = 2.78×10 −2 exp (-2.02 eV/ kT), P O 2 =0.21 atm; and Du CoO Ni (cm 2/s)=1.22×10 −2 exp (-2.15 eV/ kT), P O 2 =1.5×10 −5 atm. We discuss these results and particularly the dependence on oxygen partial pressure. The P O 2 exponent is smaller for impurity diffusion than for self-diffusion. This has been interpreted as evidence for an interaction between Ni atoms and doubly charged vacancies.

Autodiffusion en volume dans la phase plastique de l'acide pivalique (acide 2.2 dimethyl propanoique)—I: Mesure des coefficients de diffusion et de l'effet isotopique

Self-diffusion studies have been performed in the orientationally disordered or the so-called plastic phase of pivalic acid. Single crystals of high purity (99.9999%) containing 10 9−10 10 dislocations m −2 have been used. Thin layers of pivalic acid labelled with 14C or tritium were deposited on sample surfaces. Concentrationpenetration curves were established by serial sectioning. Lattice self-diffusion coefficients D, were measured from 281 to 304.75K. At 281K, the value of D is independent of time. From 281 to 301K, D is given by: D(m 2S −1) = (4.9 ± 0.3)10 −4 exp [− (59± 1) kJ mole −1/ RT]. The activation enthalpy of the lattice self-diffusion is roughly equal to the heat of sublimation ( L s = 57 kJ mole −i) and in good agreement with values obtained from NMR. The mass factor f Δ K, where f is the correlation factor and Δ K is a correction factor, has been measured using isotope effect studies. Between 281 and 301K the value obtained is fΔ K* 0.1 +0.2 −0.1

Ternary Diffusion: Restrictions on the (2D) Matrix

An analysis has been made of ternary diffusing systems to determine the possibility that individual diagonal interdiffusion coefficient elements of thek(2D) (k = 1,2,3) interdiffusion coefficient matrices can be negative. It is shown that in ternary diffusing systems, in which the concentration-penetration curves are monotonic, as many as three of the six diagonal coefficients can be negative. It is further shown that several ternary diffusing systems having a negative diagonal interdiffusion coefficient matrix element have already in fact been determined experimentally.

Autodiffusion le long des sous-joints dans la phase ‘plastique’ de l'acide pivalique (2,2-dimethyl propanoique acide)

Abstract SUB-GRAIN-BOUNDARY SELF-DIFFUSION IN ‘PLASTIC’ PIVALIC ACID (2,2-DIMETHYL PROPANOIC ACID) The sub-grain-boundary self-diffusion coefficient has been measured in the orientationally disordered (plastic) phase of pivalic acid. High purity (99·9999%) polycrystals were used. A sub-structure was introduced by compression creep of single crystals at room temperature. The average grain size was about 200 μm and the misorientation about 3°. A thin layer of tracer (molecules of pivalic acid labelled with 14C) was deposited on each sample. Concentration-penetration curves were established by the serial-sectioning technique. To calculate D′δ, where δ is the sub-grain-boundary width and D′ the sub-grain-boundary self-diffusion coefficient, Le Claire's solution was used; it describes Suzuoka's and Whipple's analysis in the case of the sectioning technique. The slope variation of concentration-penetration curves versus time of diffusion anneal shows that D′δ is characteristic of the sub-grain-boundary self-diffusion. From 281 to 297 K, D′δ is given by D′δ (m3 s−1) = (3 ± 0·7)10−9 exp[-(47 ± 3) kJ mol−1]/RT, the value 47 kJ mol−1 being the activation energy of the process which is significantly lower than the value of lattice self-diffusion activation energy, 59 ± 1 kJ mol−1. Results using the crude Fisher solution agree with this analysis of the experiments.

Diffusion composition path patterns in ternary systems

A new viewpoint on the analysis of diffusion behavior in ternary systems is presented, in which the matrix of diffusion coefficients is replaced by the “relative penetration tendencies” of the three species. An approximate but physical approach is combined with a linear approximation description of concentration-penetration curves for individual species in diffusion couples. The approximation makes the calculation of the diffusion path and Kirkendall shift for a given ternary couple very simple and straightforward: this in turn facilitates the calculation of a complete pattern of composition paths and Kirkendall shifts on the Gibbs triangle for any given model of relative penetration tendencies of the components. The availability of such patterns makes it easy to recognize and model the relative penetration tendencies in systems for which the composition path pattern has been experimentally determined.

Diffusion in the titanium-aluminium system—II. Interdiffusion in the composition range between 25 and 100 at.% Ti

Interdiffusion phenomena have been investigated m the Ti-Al system in the region from 25 to 100 at.% Ti at temperatures between 700 and 1200°C. The phase diagram of the Ti-Al system has been constructed using data from concentration-penetration curves recorded for various types of diffusion couples. In the composition range ≲ 25 at.% Al, the phase diagram is found to agree with that proposed by Blackburn. In the Al-rich part of the diagram a phase Ti 2Al 5 was found which is probably the same as the compound Ti 5Al 11 reported by Schubert et al. The growth of the various diffusion layers is non-parabolic; the reason is supposed to be the influence of grain boundary diffusion. The latter decreases steadily with increasing annealing time as a result of grain growth in the layer. Ti is the most mobile element in the Ti 3Al phase at temperatures between 768–865°C, whereas in the Al-richer compounds Al is the most mobile element at temperatures between 784–972°C.

Analysis of diffusion paths in a three-component system

The analytical solution for the case of one-dimensional diffusion in a homogeneous, three-component system, in which the diffusion coefficients are assumed to be independent of concentration, is subjected to a more detailed analysis than was given in a previous paper. An analytical relationship is derived that enables one to choose boundary conditions in such a way as to eliminate all physically meaningless special solutions containing negative concentrations. It is shown that the magnitude of the ratio of an off-diagonal coefficient to the sum of the principal diffusion coefficients may be used as one of the criteria in the procedure. Further, a generalization of the analysis enables one to specify the parameters that control the depths of minima in non-monotonic concentration-penetration curves which are physically meaningful.

Kirkendall effect and diffusion in the gold-platinum system—II: The concentration penetration curves and the diffusion coefficients

During the interdiffusion of gold and platinum a phase boundary appears, which can be seen from the concentration penetration curves; these curves are discussed in this part of the paper. The overall diffusion coefficient has been calculated from the curves according to the graphical method of Matano. From the observed Kirkendall displacement and the data concerning the concentration gradient and the concentration in the marker interface, the partial diffusion coefficients could be calculated. From the ratio between the partial diffusion coefficients a quantity has been derived which enables us to express the magnitude of an observed Kirkendall effect in a numerical value between 1 and 0.