Phase Transformation and Diffusion

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Authors: Devendra Gupta
Abstract: Engineering materials are commonly polycrystalline in nature and chemically inhomogeneous containing hetero-phases and interfaces. Because diffusion is ubiquitous in dissimilar phases and defects, it plays a vital role in the performance and reliability. During the last several decades, a synergism of the microstructural properties and chemical inhomogeniety with diffusion has been attempted to unify their apparently diverse behavior. We discuss the methodology and the thermodynamical analyses of the diffusion data needed to obtain this synergism quantitatively and illustrate it by the results obtained in a wide variety of materials, both metallic and non-metallic. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries and interfaces in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters - the enthalpy and the entropy of binding - have been extracted and levels of solute concentrations estimated. Finally, it is shown that similar analyses when applied to complex materials, e.g. the Pb-Sn eutectic alloy, the Ni3Al intermetallic compound, and an Ag-ceramic system, also result in acceptable values of interface energies and segregation factors.
Authors: Irina V. Belova, Graeme E. Murch, Thomas Fiedler, Andreas Öchsner
Abstract: In this overview, we introduce the recently developed Lattice Monte Carlo method for addressing and solving phenomenologically-based mass and thermal diffusion problems especially for composite and porous materials. With examples, we describe the application of this numerical method to calculate effective mass diffusivities and concentration profiles. Next, we describe the application of this method to the calculation of effective thermal conductivities/thermal diffusivities and temperature profiles.
Authors: G.P. Tiwari, R.S. Mehrotra
Abstract: The paper reviews the correlation between the processes of diffusion and melting. It is shown that the entropy of fusion and the melting temperature have a governing influence on the self-diffusion rates in solids. The relationship between self-diffusion coefficient (D) in solids and the melting parameters can be expressed as follows: D = fa2ν exp (κSm / R) exp (– κSmTm / RT) , where f is the correlation factor, a the lattice parameter, ν the vibration frequency, Sm the entropy of fusion, Tm the melting temperature in degree K, κ a constant and R, T have their usual meaning. The above equation has been derived on the basis that the free energy of activation for diffusion is directly proportional to the free energy of liquid phase. The well known relationships of the activation energy for self-diffusion with the melting point and enthalpy of fusion can be derived on the basis of this assumption. The constant κ is a group constant for any class or group of solids having identical physical and chemical properties. The validity of the above equation is demonstrated by the fact that when the self-diffusion coefficients are plotted as a function of homologous temperature, they scale inversely with the magnitude of the entropy of fusion. The hierarchy of self-diffusion rates within any group of solids is governed by the magnitude of the entropy of fusion and the melting temperature. The paper also discusses some interesting fall out of the close relationship between the diffusion and the melting parameters concerning (a) the diffusion in elemental anisotropic lattices, (b) anomalous diffusion behavior in bcc transition metals, lanthanides and actinides and (c) congruently melting compounds.
Authors: G.B. Kale
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.
Authors: K. Bhanumurthy, A. Laik, G.B. Kale
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.
Authors: A. Laik, K. Bhanumurthy, G.B. Kale
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.
Authors: Goutam Mohapatra, Satyam S. Sahay
Abstract: Dilatometer is often used for in situ measurement of phase transformation by monitoring the length change during heating or cooling cycle. However, the inevitable temperature gradient across the specimen length during inductive heating, introduces uncertainty in temperature measurements and hence the associated phase transformation kinetics. Due to this uncertainty, it is more meaningful to interpret the transformation kinetics from dilatometry in terms transformation ranges instead of unique values of fraction transformed. In the present work, a probabilistic approach has been used to predict the fraction transformed ranges, arising due to the temperature gradient during dilatometry. The approach has been validated for Fe-5.93 at.% Ni undergoing austenite to ferrite phase transformation at various constant cooling rates.
Authors: M.N. Mungole, Prakash C. Trivedi, Satyam Sharma, R.C. Sharma
Abstract: The recrystallization kinetic of 17Cr 1Mo ferritic steel was studied using 60% cold rolled samples. The recrystallization was carried out at 750 , 800 and 9000C for 3, 5, 15, 30 and 60 minuets. The volume fraction of the recrystallized grains was used as a kinetic parameter. The magnitude of time exponent “n” was much less than the ideal value because of the heterogeneous recrystallization. The estimated activation energy for recrystallization “Q” was more as compared to those for pure metals.
Authors: B. Jeya Ganesh, S. Raju, E. Mohandas, M. Vijayalakshmi
Abstract: The effect of thermal ageing on the heat capacity and transformation behaviour of behaviour of 9Cr-1Mo-0.1C (wt.%) ferritic / martensitic steel has been studied using differential scanning calorimetry (DSC) in the temperature range 473 to 1273 K. It is found that a-ferrite + carbide ® g-austenite phase transformation temperature is only mildly sensitive to microstructural details; but the enthalpy change associated with this phase transformation and especially, the change in specific heat around the transformation regime are found to be dependent on the starting microstructure generated by thermal ageing treatment. Prolonged ageing for about 500 to 5000 hours in the temperature range 823 to 923 K contributed to a decrease in heat capacity, as compared to the normalised and tempered sample. The martensite microstructure is found to possess the lowest room temperature CP among different microstructures.

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