Role of the Molar Volume on Estimated Diffusion Coefficients
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ON study by the diffusion couple technique is an important procedure to examine the diffusion of components.[1] Relations are developed to estimate different diffusion parameters such as the interdiffusion and the intrinsic diffusion coefficients utilizing the Kirkendall marker experiments.[2–7] The tracer diffusion coefficients could be estimated indirectly if the thermodynamic parameters accounting the chemical driving forces for the diffusing components are known.[8] This technique has an added advantage that one can design experiments mimicking the material systems in real applications. It is already established that the deviation of molar volume from the ideality with the variation of composition affects (in general adversely) the material systems. Positive or negative deviation leads to expansion or shrinkage in the total volume, which could be reasonably large in many systems. This is important in many applications, in which the performance of the product depends on the diffusion-controlled growth of the phases such as materials in electronic packaging,[9] A15 intermetallic superconductors,[10] and bond coat in jet engines.[11] Additionally, this brings major comSANGEETA SANTRA, PhD Student, and ALOKE PAUL, Associate Professor, are with the Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India. Contact e-mail: [email protected] Manuscript submitted January 15, 2015. Article published online June 13, 2015 METALLURGICAL AND MATERIALS TRANSACTIONS A
plications for the estimation of the diffusion parameters. For the interdiffusion coefficients, a primary requisite of the Matano–Boltzmann (MB) treatment is locating the initial contact plane (bonding plane) of the diffusion couple.[12] However, it is almost impossible to locate this plane exactly when the system undergoes a volume change. Similarly, Heumann[6] developed a relation for the estimation of the ratio of intrinsic diffusion coefficients at the Kirkendall marker plane, which also needs to locate the initial contact plane. To circumvent this problem, Sauer–Freise (SF),[3] den Broeder (dB),[4] and Wagner[5] developed the relations in which there is no need to locate the initial contact plane for the estimation of the interdiffusion coefficients. Similarly, van Loo developed a relation to estimate the ratio of the intrinsic diffusion coefficients.[7] Although relations are developed that avoid the prerequisite knowledge of the location of the initial contact plane facilitating the use of actual variation of the molar volume, it is not so uncommon to find the use of the MB treatment for interdiffusion coefficients and Heumann’s method for the intrinsic diffusion coefficients. These are used mainly in the systems in which the molar volume does not deviate much from the ideal value.[13] However, there are numerous systems in which the molar volume deviates significantly.[14] In ternary systems, because of the unavailability of lattice parameter data, there is no room for using more accurate methods anyway. Moreover, different treatments could impart
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