Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

Mutual diffusion coefficients of some binary liquid systems: benzene-n-alkyl alcohol

The mutual diffusion coefficients for binary liquid systems of benzene-n-alkyl alcohol at various compositions have been determined by the diaphragm cell method at 28-degrees-C. The alcohols used were the members of n-paraffinic alcohols ranging from C1 to C8. The maximum possible experimental error is 14%. The data were fitted with a generalized correlation, giving the deviation from the experimental data to within 2.75%, on average.

Estimation of intrinsic diffusion coefficients in a pseudo-binary diffusion couple

Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in multi-component systems is developed utilizing the concept of a pseudo-binary approach. This is explained with the help of experimentally developed diffusion profiles in the Cu(Sn, Ga) and Cu(Sn, Si) solid solutions. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Role of the Molar Volume on Estimated Diffusion Coefficients

The role of the molar volume on the estimated diffusion parameters has been speculated for decades. The Matano-Boltzmann method was the first to be developed for the estimation of the variation of the interdiffusion coefficients with composition. However, this could be used only when the molar volume varies ideally or remains constant. Although there are no such systems, this method is still being used to consider the ideal variation. More efficient methods were developed by Sauer-Freise, Den Broeder, and Wagner to tackle this problem. However, there is a lack of research indicating the most efficient method. We have shown that Wagner's method is the most suitable one when the molar volume deviates from the ideal value. Similarly, there are two methods for the estimation of the ratio of intrinsic diffusion coefficients at the Kirkendall marker plane proposed by Heumann and van Loo. The Heumann method, like the Matano-Boltzmann method, is suitable to use only when the molar volume varies more or less ideally or remains constant. In most of the real systems, where molar volume deviates from the ideality, it is safe to use the van Loo method. We have shown that the Heumann method introduces large errors even for a very small deviation of the molar volume from the ideal value. On the other hand, the van Loo method is relatively less sensitive to it. Overall, the estimation of the intrinsic diffusion coefficient is more sensitive than the interdiffusion coefficient.

Diffusion Parameters in the Nb-Mo System: Revisited

The variation of the interdiffusion coefficient with the change in composition in the Nb-Mo system is determined in the temperature range of 1800 °C to 1900 °C. It was found that the activation energy has a minimum at around 45 at. pct Nb. The values of the pre-exponential factor and the activation energy for diffusion are compared with the data available in the literature. Further, the impurity diffusion coefficients of Nb in Mo and Mo in Nb are calculated.

Topological close packed mu phase formation and the determination of diffusion parameters in the Co-Mo system

The study on the formation and growth of topological close packed (TCP) compounds is important to understand the performance of turbine blades in jet engine applications. These deleterious phases grow mainly by diffusion process in the superalloy substrate. Significant volume change was found because of growth of the p phase in Co-Mo system. Growth kinetics of this phase and different diffusion parameters, like interdiffusion, intrinsic and tracer diffusion coefficients are calculated. Further the activation energy, which provides an idea about the mechanism, is determined. Moreover, the interdiffusion coefficient in Co(Mo) solid solution and impurity diffusion coefficient of Mo in Co are determined.

Growth mechanism of phases by interdiffusion and diffusion of species in the niobium-silicon system

The integrated diffusion coefficient of the phases and the tracer diffusion coefficients of the species are determined in the Nb-Si system by the diffusion couple technique. The diffusion rate of Si is found to be faster than that of Nb in both the NbSi2 and Nb5Si3 phases. The possible atomic mechanism of diffusion is discussed based on the crystal structure and on available details of the defect concentration data. The faster diffusion rate of Si in the Nb5Si3 phase is found to be unusual. The growth mechanism of the phases is also discussed on the basis of the data calculated in this study. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Diffusion Parameters and Growth Mechanism of Phases in the Cu-Sn System

The tracer diffusion coefficients of the elements as well as the integrated interdiffusion coefficients are determined for the Cu3Sn and Cu6Sn5 intermetallic compounds using incremental diffusion couples and Kirkendall marker shift measurements. The activation energies are determined for the former between 498 K and 623 K (225 A degrees C and 350 A degrees C) and for the latter between 423 K and 473 K (150 A degrees C and 200 A degrees C). Sn is found to be a slightly faster diffuser in Cu6Sn5, and Cu is found to be the faster diffuser in Cu3Sn. The results from the incremental couples are used to predict the behavior of a Cu/Sn couple where simultaneous growth of both intermetallics occurs. The waviness at the Cu3Sn/Cu6Sn5 interface and possible reasons for not finding Kirkendall markers in both intermetallics in the Cu/Sn couple are discussed.

Diffusion of sorbates in zeolites Y and A novel dependence on sorbate size and strength of sor ba t e-Zeoli t e interaction

A systematic investigation of monatomic spherical sorbates in the supercages of zeolites Y and A by molecular dynamics technique is presented. Rates of intercage diffusion, rates of cage visits, and the diffusion coefficients have been calculated as a function of the sorbate-zeolite interaction strength. These properties exhibit markedly different dependences on interaction strength for the two zeolites. The observed behavior is shown to be a consequence of the two principal mechanisms of intercage diffusion and the energetic barrier associated with them. The diffusion coefficient and other properties associated with intercage diffusion are found to be directly proportional to the reciprocal of the square of the sorbate diameter when the sorbate diameter is significantly smaller than the window diameter. As the sorbate diameter increases, a peak is observed in all the transport properties investigated including the diffusion coefficient. We call this surprising effect as the ring or levitation effect and it explains several anomalous results reported in the literature and suggests a breakdown of the geometrical criterion for diffusion of sorbates. It shows that under certain conditions nongeometrical factors play a major role and geometrical factors become secondary in the determination of the molecular sieve property. A generalized parameter has been proposed which suggests conditions under which one can expect the ring or levitation effect in any porous medium. Inverse size selectivity becomes operative under these conditions.

Shear-induced enhancement of self-diffusion in interacting colloidal suspensions

We set up the generalized Langevin equations describing coupled single-particle and collective motion in a suspension of interacting colloidal particles in a shear how and use these to show that the measured self-diffusion coefficients in these systems should be strongly dependent on shear rate epsilon. Three regimes are found: (i) an initial const+epsilon(.2), followed by (ii) a large regime of epsilon(.1/2) behavior, crossing over to an asymptotic power-law approach (iii) D-o - const x epsilon(.-1/2) to the Stokes-Einstein value D-o. The shear dependence is isotropic up to very large shear rates and increases with the interparticle interaction strength. Our results provide a straightforward explanation of recent experiments and simulations on sheared colloids.

Diffusion and Growth of the mu Phase (Ni6Nb7) in the Ni-Nb System

Incremental diffusion couple experiments are conducted to determine the average interdiffusion coefficient and the intrinsic diffusion coefficients of the species in the Ni6Nb7 (mu phase) in the Ni-Nb system. Further, the tracer diffusion coefficients are calculated from the knowledge of thermodynamic parameters. The diffusion rate of Ni is found to be higher than that of Nb, which indicates higher defect concentration in the Ni sublattice.

Growth mechanism of phases by interdiffusion and atomic mechanism of diffusion in the molybdenum-silicon system

Tracer diffusion coefficients are calculated in different phases in the Mo-Si system from diffusion couple experiments using the data available on thermodynamic parameters. Following, possible atomic diffusion mechanism of the species is discussed based on the crystal structure. Unusual diffusion behaviour is found in the Mo(5)Si(3) and Mo(3)Si phases, which indicate the nature of defects present on different sublattices. Further the growth mechanism of the phases is discussed and morphological evolution during interdiffusion is explained. (C) 2011 Elsevier Ltd. All rights reserved.

Reactive Diffusion Between Vanadium and Silicon

Interdiffusion study is conducted in the V-Si system to determine integrated diffusion coefficients of the phases. Activation energy values are calculated from the experiments conducted at different temperatures. The average values are found to be 208, 240 and 141 kJ/mol, respectively, for the V(3)Si, V(5)Si(3) and VSi(2) phases. The low activation energy for the VSi(2) phase indicates very high concentration of defects or the significant contribution from the grain boundary diffusion. The error in calculation of diffusion parameters from a very thin phase layer in a multiphase diffusion couple is discussed. Further the data available in the literature in this system is compared and the problems in the indirect methodology followed previously to calculate the diffusion parameters are discussed.

Growth mechanism of the Nb(X)Si-2 and [Nb(X)](5)Si-3 phases by reactive diffusion in Nb (X = Ti, Mo, or Zr)-Si systems

The effects of Mo, Ti, and Zr on the diffusion and growth of the Nb(X)Si-2 and Nb(X)(5)Si-3 phases in an Nb(X)-Si system are analyzed. The integrated diffusion coefficients are determined from diffusion couple experiments and compared with the data previously calculated in a binary Nb-Si system. The growth rates of both phases are affected by the addition of Mo and Zr, whereas the addition of Ti has no effect. The atomic mechanism of diffusion is also discussed based on the crystal structure and the possible changes in the defect concentrations due to alloying. Finally, the growth mechanism of the phases is discussed on the basis of a physico-chemical approach. (C) 2011 Elsevier Ltd. All rights reserved.