A method for determination of [D] in ternary systems from a single experiment

A method is presented for the calculation of [D] from a single interdiffusion experiment. The procedure, lhich is limited to cases lhere [D] is an essentially constant function of compositions, is illustrated for arbitrary concentration distributions.     

Multiphase binary diffusion in infinite and semi-infinite media: Part I. On the determination of interdiffusion coefficients

Mathematical relationships describing the multiphase binary diffusions are deduced under the condition that in an infinite medium, and also under the condition that and the fluxes of both the species occur in each other’s opposite direction through the surface in a semi-infinite medium, where are the interdiffusion coefficient and the partial molal volume of componenti in phasej, respectively, and are composition independent. Two graphical evaluation methods for obtaining the interdiffusion coefficients for all the phases present in the diffusion zone have been developed in infinite and semi-infinite media. Concentration-distance curves of both the components for an infinite medium and those curves and also mass change of the couple per unit area of the surface before and after the diffusion anneal for a semi-infinite medium must be prepared to calculate an interdiffusion coefficient for each phase.     

Improving the calculation of interdiffusion coefficients

Least-squares spline interpolation techniques are reviewed and presented as a mathematical tool for noise reduction and interpolation of diffusion profiles. Numerically simulated diffusion profiles were interpolated using a sixth-order spline. The spline fit data were successfully used in conjunction with the Boltzmann-Matano treatment to compute the interdiffusion coefficient, demonstrating the usefulness of splines as a numerical tool for such calculations. Simulations conducted on noisy data indicate that the technique can extract the correct diffusivity data given compositional data that contain only three digits of information and are contaminated with a noise level of 0.001. Splines offer a reproducible and reliable alternative to graphical evaluation of the slope of a diffusion profile, which is used in the Boltzmann-Matano treatment. Hence, use of splines reduces the numerical errors associated with calculation of interdiffusion coefficients from raw diffusion profile data.     

Evaluation of an empirical representation of ternary diffusion paths in a system with constant diffusion coefficients

An empirical two-parameter representation of ternary diffusion paths has been proposed by Dayananda and Kim. Their proposal has been tested on a hypothetical ternary diffusing system with constant diffusion coefficients for which the exact diffusion paths can be calculated analytically. It is found that the error in using the two-parameter representation rather than the true diffusion path is strongly dependent on the value of the ratio of the terminal relative concentration differences of the diffusion couple selected for analysis.     

Experimental determination of ternary partition coefficients in Fe-Ni-X alloys

A directional solidification experiment to measure partition coefficients of ternary additions in Fe-Ni alloys is described. A model is developed to calculate the extent of solid state diffusion effects during and after solidification. Ternary diffusivities of Ge and Au in Fe-Ni were measured for use in the calculation procedure. The model is used to correct the measured partition coefficients for solid state diffusion effects. The resulting equilibrium partition coefficients, K _x ^o , for elementX in Fe-Ni-X alloys are 0.43 for Au, 0.58 for Ge, 0.12 for P, 0.87 for Ni, and 1.45 for Pt. These studies demonstrated that solid state diffusion effects are significant when the diffusivity of the third elementX, in Fe-Ni, is higher than 1 × 10⁻¹⁰ cm²/s at 1300 °C. The partition coefficient data is of particular interest in understanding the fractionation behavior of trace elements in iron meteorites.     

局域平衡原理与相图的扩散偶法测定

介绍了局域平衡原理和扩散偶法测定平衡相图的方法要点.扩散偶法是一种高效的、可靠的相图测定方法,它可以大幅度减少实验工作量,减少原材料消耗,加快相图实测进程.此外,这种方法还具有可直接测定相平衡关系、相平衡成分,避免“过冷效应”等优点,特别适合于多组元系统平衡相图的实验测定.     

Gamete donation from couple to couple in the new French law

In practice, the partners or spouses of gamete donors are frequently asked permission for the donation. The new French law on bioethics of 29 July 1994 requires that: a) the donor should be one of a couple that has already procreated and b) the written consent of the partner or spouse is obtained. These conditions lead not only to several practical problems in the organisation of donor insemination but also reject a large part of the potential donor population. The two basic qualities demanded of the donors, e.g., paternity and stable relationship, are analyzed. It is proposed that only fatherhood should serve as an exclusionary criterion for sperm donation. The donor need not be a part of a couple at the moment of the donation but if he has a partner at that time her opinion should be heard.     

Application of the diffusion couple to study phase equilibria in the Fe-Cr-S ternary system at 600 °C

The sulfidation of Fe-Cr alloys has a large financial significance for industries that use fossil fuels, such as the electric utility industry. Therefore, the sulfidation of a series of Fe-Cr alloys was studied at 600 °C using a solid-state diffusion couple technique. The diffusion couple technique combined Fe_0.95S powder and FeCr binary alloys together in a configuration that allowed for post-heat-treatment microanalysis using an electron probe microanalyzer (EPMA). The results showed that only two different diffusion couple microstructures formed in samples spanning the entire Fe-Cr binary range. The Fe-rich alloy diffusion couples contained a surface αFeCr layer and an internal sulfide precipitate layer that contained three different sulfide phases. The Cr-rich alloy diffusion couples also possessed an internal precipitate layer, as well as a thick, triplex interfacial scale. The ternary elemental diffusion was described using diffusion paths plotted on the 600 °C isothermal section of the Fe-Cr-S phase diagram. The results also showed that samples with less than 51 wt Pct Cr were more sulfidation resistant. The accuracy of the existing Fe-Cr-S 600 °C isothermal section was assessed, and it was determined that the τ phase field had a larger composition than previously published.     

A theoretical analysis for the formation of periodic layered structure in ternary diffusion couples involving a displacement type of reactions

Periodic layered structures were found to form in numerous ternary diffusion couples of the type B_δ′C/A involving a displacement type of reactions. In all of these couples, A is a dominant diffusing species within the diffusion zone and C is essentially immobile. Occurrence of this type of layered structure was rationalized in terms of thermodynamic arguments. Moreover, a diffusion model was formulated to describe the growth of this structure. An appropriate solution to the diffusion equations was obtained when simplified assumptions were made. The relative stability of a periodic layered structure versus that of a simple layered structure is governed by the relative mobilities of A and B within the diffusion zone. The simple layered structure is formed when B has a high mobility relative to that of A. On the other hand, with increasing mobility of A, the periodic layered structure tends to be stable.     

An interdiffusion study of a NiAl alloy using single-phase diffusion couples

The intermetallic compound NiAl is highly ordered at stoichiometry, even at high temperatures. For instance, its point-defect concentration at 900 °C is on the order of 10⁻³ at this composition. Moreover, its enthalpy of formation is highly negative and exhibits a minimum at stoichiometry. All of these data suggest that the interdiffusion coefficient should exhibit a minimum at this composition. Yet, the literature data show that the minimum interdiffusion coefficient occurred between 48 and 49 at. pct Al. Accordingly, we have carried out diffusion-couple measurements employing single-phase NiAl wafers over the temperature interval from 700 °C to 1000 °C. The measured concentration profiles were analyzed in terms of the lattice mole fraction, yielding interdiffusion coefficients as a function of composition and temperature. For all the temperatures studied, the interdiffusion coefficients were found to exhibit a minimum at the stoichiometric composition, with a corresponding maximum in the activation energies obtained from the temperature dependence of the interdiffusion coefficients.     

Formation of intermetallics in a porous powder titanium-nickel diffusion couple

A method of fabricating porous powder Ti-Ni diffusion couples was developed, and the structure of the diffusion zone in these after isothermal annealing at 1073, 1173, and 1273 K studied. Microstructural analysis and microhardness measurements revealed that the width of the diffusion zone and the thickness of the intermetallic layers increased with increasing temperature. Mutual diffusion coefficients were calculated, and an explanation proposed for the more rapid intermetallic layer growth in porous powder than in solid diffusion couples above 1173 K. This was related to the presence of rapid diffusion paths (surfaces, grain boundaries) which persisted at high temperatures in the porous powder diffusion couples, while those in solid couples (point and line defects) were eliminated when the temperature was raised.Samarsk State Aerospace University. Translated from Poroshkovaya Metallurgiya, Nos. 5/6, pp. 62–70, May–June, 1995.     

A new treatment for determining the activities from ternary miscibility gap: The O-Cu-Pb system

TheR function is used to develop Choudary and Chang's method for calculating activities of compo-nents along the miscibility gap in the ternary systems consisting of two metals and a nonmetal. In this new treatment, the knowledge of the tie-line distribution within a two phase region and the graphical integration, which both are required by normal methods, are not necessary. Therefore, it will give more precise results and more applications.     

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.     

Measurement of liquid metal diffusion coefficients from steady-state solidification experiments

Steady state solidification experiments were carried out on Sn?Bi alloys of compositions from zero to 3.5 at. pet Bi with tube diameters from 1.9 to 5 mm. Solute profiles were determined utilizing a radioiostope, Bi²⁰⁷, and a microtome slicing technique. Results indicate the technique offers a relatively precise method for determining liquid metal diffusion coefficients at the solidus temperature. Convection does not appear to be a problem for tube diameters under 3 mm. It is shown that neglect of thermal transport may give errors in the measured diffusion coefficients as high as 10 to 30 pet.     

Single-particle tracking: the distribution of diffusion coefficients

In single-particle tracking experiments, the diffusion coefficient D may be measured from the trajectory of an individual particle in the cell membrane. The statistical distribution of single-trajectory diffusion coefficients is examined by Monte Carlo calculations. The width of this distribution may be useful as a measure of the heterogeneity of the membrane and as a test of models of hindered diffusion in the membrane. For some models, the distribution of the short-range diffusion coefficient is much narrower than the observed distribution for proteins diffusing in cell membranes. To aid in the analysis of single-particle tracking measurements, the distribution of D is examined for various definitions of D and for various trajectory lengths.     

Method of assessing diffusion coefficients from gas absorption by metal powders

Conclusions A simple experimental method is proposed for determining diffusion coefficients from amounts of gas absorbed by metal powders. An analysis is made of errors in the measurement of D by the new method, and optimum experimental conditions are indicated. Data yielded by a study of the diffusion of hydrogen in LaCo₅ show that D _H ²⁹³ LaCo₅ can be calculated by this method with satisfactory accuracy.Translated from Poroshkovaya Metallurgiya, No. 4(232), pp. 25–32, April, 1982.     

An analysis of interdiffusion in finite-geometry,two-phase diffusion couples in the Ni−W and Ag−Cu systems

The progress of homogenization in finite, multilayer diffusion couples was studied experimentally using both quantitative metallography to measure phase thicknesses and electron microprobe analysis to determine concentration-distance profiles. Ni?W couples having mean compositions in the nickel-rich terminal solid solution range (12.1 and 15.2 at. pct W) were studied after 4.43 to 240.7 hr interdiffusion treatments at 1156° and 1207°C. Ag?Cu couples having mean compositions in both of the terminal solid solution ranges (8.5 at. pct Cu and 2.1 at. pct Ag) were studied after 3.8 to 65.4 hr interdiffusion treatments at 760°C. Experimental data were in good agreement with calculations of interdiffusion based on equilibrium interface concentrations and concentration-independent interdiffusion coefficients. The good agreement between experimental data and calculated values for the Ni?W couples extended to times necessary for the achievement of essentially complete homogenization,i.e., through both the two-phase dissolution process and the subsequent stage of gradient elimination in the terminal solid solution phase.