Aloke Paul

Thermodynamics, diffusion and the Kirkendall effect in solids

Thermodynamics, phases and phase diagrams.- Structure of Materials.- Ficks laws of diffusion.- Development of interdiffusion zone in different systems.- Atomic mechanism of diffusion.- Interdiffusion and the Kirkendall effect in binary systems.- Growth of phases with narrow homogeneity range and line compounds by interdiffusion.- Microstructural evolution of the diffusion zone.- Interdiffusion in multicomponent systems.- Short circuit diffusion.- Reactive phase formation in thin film systems.

Intermetallic growth and Kirkendall effect manifestations in Cu/Sn and Au/Sn diffusion couples

Abstract The Kirkendall-effect induced migration of inert markers during a diffusion-controlled growth of intermetallic compounds in the Cu/Sn and Au/Sn couples at 215 and 180°C were studied. It was shown that the behaviour of markers in the multiphase reaction zones can be rationalized in terms of the Kirkendall velocity construction. Observations on the microstructural features of the product intermetallic layers and the role of the Kirkendall effect in the morphogenesis of the interdiffusion systems are discussed. It was demonstrated that the velocity of markers in a product layer, the appearance of the Kirkendall plane(s), their location(s) and the morphological evolution of the reaction products can also be explained from a purely chemical point of view considering the diffusion-controlled interactions at the interphase interfaces. A representation of the reaction scheme and kinetics of intermetallic growth in each of the two systems is given.

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.

Growth mechanism of tantalum silicides by interdiffusion

Interdiffusion studies were conducted to understand the atomic mechanism of the diffusing species and the growth mechanism of the phases. Integrated diffusion coefficients and the ratio of tracer diffusion coefficients were estimated for these analyses. The activation energies for the integrated diffusion coefficients were calculated as 550 ± 70 and 410 ± 39 kJ/mol in the TaSi2 and Ta5Si3 phases, respectively. In the TaSi2 phase, Ta has a slightly lower but comparable diffusion rate with respect to Si, although no Ta–Ta bonds are present in the crystal. In the Ta5Si3 phase, Si has a higher diffusion rate, which is rather unusual, if we consider the atoms in the nearest-neighbour positions for both the elements. The ratio of Si to Ta tracer diffusion coefficients is found to be lower in the Si-rich phase, TaSi2, compared to the Si-lean phase, Ta5Si3, which is also unusual. This indicates the type of structural defects present. An analysis on the growth mechanism of the phases indicates that duplex morphology and the Kirkendall marker plane should only be present in the TaSi2 phase. This is not present in the Ta5Si3 phase due to the very high growth rate of the TaSi2 phase, which consumes most of the Ta5Si3 phase layer. The problems in the calculation method used previously by others in this system are also explained.

Effect of Ni content on the diffusion-controlled growth of the product phases in the Cu(Ni)-Sn system

Abstract A strong influence of Ni content on the diffusion-controlled growth of the (Cu,Ni)3Sn and (Cu,Ni)6Sn5 phases by coupling different Cu(Ni) alloys with Sn in the solid state is reported. The continuous increase in the thickness ratio of (Cu,Ni)6Sn5 to (Cu,Ni)3Sn with the Ni content is explained by combined kinetic and thermodynamic arguments as follows: (i) The integrated interdiffusion coefficient does not change for the (Cu,Ni)3Sn phase up to 2.5 at.% Ni and decreases drastically for 5 at.% Ni. On the other hand, there is a continuous increase in the integrated interdiffusion coefficient for (Cu,Ni)6Sn5 as a function of increasing Ni content. (ii) With the increase in Ni content, driving forces for the diffusion of components increase for both components in both phases but at different rates. However, the magnitude of these changes alone is not large enough to explain the high difference in the observed growth rate of the product phases because of Ni addition. (iv) Kirkendall marker experiments indicate that the Cu6Sn5 phase grows by diffusion of both Cu and Sn in the binary case. However, when Ni is added, the growth is by diffusion of Sn only. (v) Also, the observed grain refinement in the Cu6Sn5 phase with the addition of Ni suggests that the grain boundary diffusion of Sn may have an important role in the observed changes in the growth rate.

A pseudo-binary interdiffusion study in the beta-Ni(Pt)Al phase

Interdiffusion study is conducted in the Ni-rich part of the β-Ni(Pt)Al phase following the pseudo-binary approach. Interdiffusion coefficients over the whole composition range considered in this study increases with increase in Pt content, which is in line with the theoretical study predicting the decrease in vacancy formation and migration energy because of Pt addition. The trend of change in diffusion coefficient with the increase in Ni and Pt contents indicates that Pt preferably replaces Ni antisites.

Interdiffusion and Growth of the Phases in CoNi/Mo and CoNi/W Systems

Deleterious topological-closed-packed (tcp) phases grow in the interdiffusion zone in turbine blades mainly because of the addition of refractory elements such as Mo and W in the Ni- and Co-based superalloys. CoNi/Mo and CoNi/W diffusion couples are prepared to understand the growth mechanism of the phases in the interdiffusion zone. Instead of determining the main and cross-interdiffusion coefficients following the conventional method, we preferred to determine the average effective interdiffusion coefficients of two elements after fixing the composition of one element more or less the same in the interdiffusion zone. These parameters can be directly related to the growth kinetics of the phases and shed light on the atomic mechanism of diffusion. In both systems, the diffusion rate of elements and the phase layer thickness increased because of the addition of Ni in the solid solution phase, probably because of an increase in driving force. On the other hand, the growth rate of the μ phase and the diffusion coefficient of the species decreased because of the addition of Ni. This indicates the change in defect concentration, which assists diffusion. Further, we revisited the previously published Co-Ni-Mo and Co-Ni-W ternary phase diagrams and compared them with the composition range of the phases developed in the interdiffusion zone. Different composition ranges of the tcp phases are found, and corrected phase diagrams are shown. The outcome of this study will help to optimize the concentration of elements in superalloys to control the growth of the tcp phases.

Reactive diffusion in the Ti–Si system and the significance of the parabolic growth constant

Solid diffusion couple experiments are conducted to analyse the growth mechanism of the phases and the diffusion mechanism of the components in the Ti–Si system. The calculation of the parabolic growth constants and the integrated diffusion coefficients substantiates that the analysis is intrinsically prone to erroneous conclusions if it is based on just the parabolic growth constants determined for a multiphase interdiffusion zone. The location of the marker plane is detected based on the uniform grain morphology in the TiSi2 phase, which indicates that this phase grows mainly because of Si diffusion. The growth mechanism of the phases and morphological evolution in the interdiffusion zone are explained with the help of imaginary diffusion couples. The activation enthalpies for the integrated diffusion coefficient of TiSi2 and the Si tracer diffusion are calculated as 190 ± 9 and 197 ± 8 kJ/mol, respectively. The crystal structure, details on the nearest neighbours of the components, and their relative mobilities indicate that the vacancies are mainly present on the Si sublattice.

Interdiffusion and solid solution strengthening in Ni–Co–Pt and Ni–Co–Fe ternary systems

Diffusion couple experiments are conducted in Co–Ni–Pt system at 1200 °C and in Co–Ni–Fe system at 1150 °C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co–Ni–Pt system, whereas in the Co–Ni–Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.

Vacancy wind effect on interdiffusion in a dilute Cu(Sn) solid solution

A study has been conducted on a Cu(Sn) solid solution to examine the role of the vacancy wind effect on interdiffusion. First, the interdiffusion and the intrinsic diffusion coefficients are calculated. The trend of the interdiffusion coefficients is explained with the help of the driving force. Following this, the tracer diffusion coefficients of the species are calculated with and without consideration of the vacancy wind effect. We found that the role of the vacancy wind is negligible on the minor element in a dilute solid solution, which is the faster diffusing species in this system and controls the interdiffusion process. However, consideration of this effect is important to understand the diffusion rate of the major element, which is the slower diffusing species in this system.