Papers by Author: G.B. Kale

Abstract: High temperature beta-phase in titanium and zirconium alloy systems decomposes through an eutectoid reaction into a Ti- and Zr-rich a-solid solution and an intermetallic compound. The present paper reports the layer growth kinetics of the b-solid solution phase in elemental diffusion couples of titanium and zirconium. The growth kinetics obeys a parabolic growth law. However, the temperature dependence of the growth rate constant shows a bimodal behavior. The Arrhenius plot of the growth rate constant, which is linear at the start, becomes curved at lower temperature ranges. The deviation from the Arrhenius plot of the growth rate constant is related to the curvature in the solvus line of the b-solid solution. A theoretical model for the reaction diffusion responsible for the growth of b-solid solution is presented. The growth rate of b-phase is described by the equation 2 2 . . W k D C t b = = b D x , where k is a growth rate constant and Wb is the thickness of the b-phase formed over a period of time t, Db is the interdiffusion coefficient for the b-phase, DC is concentration range of b-phase and x is a parameter which is a function of the miscibility gaps in the phase diagram on the either side of the b-phase. The above equation provides a satisfactory description of the various aspect of the phenomenon of the growth of b-phase in Ti-and Zr-alloy systems.

Abstract: The solid state diffusion characteristics in the Cu(Al) solid solution phase, was investigated in the temperature range of 1023–1223 K using single phase bulk diffusion couples between pure Cu/Cu- 10 at.% Al. The interdiffusion coefficients, D, were calculated using Boltzmann–Matano method and Hall’s method from the concentration profiles of the couples that were determined using EPMA. The interdiffusion coefficients (D) calculated ranges between 1.39 X 10−14 and 3.97 X 10−13 m2/s in the temperature range of 1023 to 1223 K. The composition and temperature dependence of D were established. The activation energy for interdiffusion varies from 123.1 to 134.2 kJ/mol in the concentration range 1 at. % ≤ CAl ≤ 9 at. %. The impurity diffusion coefficient of Al in Cu is determined by extrapolating the interdiffusion coeffficient values to infinite dilution of the alloy i.e CAl →0 and its temperature dependence was also established. The activation energy for impurity diffusion of Al in Cu was found to be 137.1 kJ/mol.

Abstract: The incremental diffusion couples are used for evaluating interdiffusion couples in a narrow composition range and these results are extrapolated to get an estimate of impurity diffusion coefficients. In fact, several incremental couples are needed to get impurity diffusion coefficients at different compositions. This process is generally tedious. The present method describes a relatively simple method for evaluating the diffusion coefficients using “step diffusion couples”. A simple experimental method is described to prepare a step diffusion couple. This method involves preparation of diffusion couples in two stages. In the first stage, diffusion couple is made between the two materials in a conventional way and annealed for extended period of time to have a large diffusion zone typically of the order of 2-3 mm. In the second stage, the starting materials are placed on the diffusion couple in a direction perpendicular to the diffusion zone and annealed at a suitable temperature for diffusion to occur between the diffusion zone and the starting materials. This method is applied to study the interdiffusion behavior in the b phase of the Ti-Zr system. Boltzmann-Matano and Hall’s methods were used to determine the interdiffusion coefficients and their composition dependence. Kirkendall shift is observed towards Ti side and the intrinsic diffusion coefficients of Ti is approximately three times that of Zr. The width of the diffusion zone is strongly dependent on the composition of the step diffusion couple. It is observed that the interdiffusion coefficients evaluated at the terminal compositions matched well those published values in the Ti-Zr system. This experimental technique offers an easy and elegant method to determine the diffusion parameters without the tedious preparation of incremental diffusion couples.

Abstract: A new form of diffusion coefficient termed as thermodynamic diffusion coefficient is introduced in this paper. Conventionally, diffusion coefficients are evaluated using concentration gradient as driving force. But truly, chemical potential gradient is the actual driving force that determines the material flow in any part of the system. Thermodynamic diffusion coefficients are based on chemical potential gradient as driving force. The relation between thermodynamic diffusion coefficients and phenomenological coefficients has been established. The advantages of thermodynamic diffusion coefficients have been underlined, especially, in the cases of line compounds where concentration difference across the phase is zero or in case of intermetallic compounds with narrow homogeneity range. The intrinsic thermodynamic diffusion coefficients are equal to tracer diffusion coefficients. This helps in estimating tracer diffusivities in cases where tracers are not easily available. The advantages of thermodynamic diffusion coefficients are shown in binary and ternary systems by illustrating them in Ni-Al and Fe-Ni-Cr systems.