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.

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Authors: G.P. Tiwari, Osamu Taguchi, Yoshiaki Iijima, 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.

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Authors: G.P. Tiwari, G.L. Goswami, S.K. Jha

245

Authors: G.P. Tiwari, V.D. Alur, E. Ramadasan

Abstract: This paper presents hydrogen concentration profiles in notched tensile test specimens which have been charged electrolytically with hydrogen, with and without the application of a tensile load. A standard 8mm ASTM tensile specimen, extended at one end, is employed. This extended portion serves as a cathode during electrolytic charging. In order to facilitate the application of a load during charging, the specimen is firmly held in a specially designed fixture with the help of threads that are provided on each end of the gauge section. A notch is provided, in the gauge section, to create a stress gradient. At the end of charging, 3mm-thick disc specimens are cut from the specimen and analyzed for their hydrogen content using the inert gas fusion technique. The results show that the presence of tensile stress enhances the rate of hydrogen ingress as well as the net hydrogen concentration in the matrix. In the absence of stress, diffusion down the concentration gradient controls the hydrogen distribution within the specimen. Surface area plays an important role in the accumulation of hydrogen across any section in the specimen. If the available surface area is greater, the local hydrogen concentration is enhanced. Sheathing of the charging section with a 3mm-thick jacket of pure uranium causes a significant improvement in the hydrogen concentration along the entire length of the specimen. However, the presence of a 100µm-thick coating of titanium in the charging section of the specimen did not cause any significant change in the hydrogen concentration of the specimen.
The main advantage of this charging procedure is that the test portion of the specimen does not come into contact with the electrolyte, and the hydrogen reaches the test portion of the specimen via diffusion through the matrix. Hence, microstructural damage to the specimen during the entry of high-fugacity hydrogen into the matrix is avoided.

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