Electromigration of hydrogen and deuterium in tantalum: Isotope effect
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I.
INTRODUCTION
THE mass transport phenomenon in condensed phases such as metals and alloys is described by electromigration. The combined influence of electronic conduction and diffusion make electromigration dependent on the electronic, spatial, and vibrational aspects of the local defects. Electromigration studies have been made for a wide range of metals over the last thirty years and interesting results have been observed, especially in case of hydrogen isotope electromigration is some metals. This work aims at observing the transport of these isotopes in tantalum. It is important to study this phenomenon in the low solid-solution concentration range where the results could well restrict the versatility of this otherwise excellent corrosion resistant, high-temperature ductile metal. On the other hand, electromigration has been used as a purification process for tantalum, besides various other methods to achieve high purity, l Electromigration driving force: The velocity of migration v of solutes is directly proportional to the applied electric force F, mathematically shown as B = v/F
[1]
where the proportionality constant B, known as absolute mobility, is a measure of the resistance to atomistic transport in the lattice. At steady-state, the external driving force is also linearly related to the applied electric field E, written as F = eZ*E
[2]
where the constant of proportionality is the effective charge eZ*. The measurement of the absolute mobility B is an experimental impossibility, except in the case of diffusion. The B. MISHRA, formerly with the Department of Chemical Engineering and Materials Science, is Research Assistant, Mineral Resources Research Center, and J.M. SIVERTSEN, Associate Professor, Department of Chemical Engineering and Materials Science, are both with the University of Minnesota, Minneapolis, MN 55455. Manuscript submitted January 18, 1983. METALLURGICALTRANSACTIONS A
Nernst-Einstein's relation relates the absolute mobility and diffusional transport by D = BkT(1 + d In 7/d In c)
[3]
whare k is the Boltzmann's constant, T is the absolute temperature, 7 is the activity coefficient, and c is the solute concentration. In the case of an ideal solution the activity coefficient is constant and the above equations yield UkT Z* = - De
[4]
where U is the electric mobility given as the migration velocity per unit applied electric field, Z* is the effective valence, and e is the fundamental electronic charge. Equation [4] requires that the force on the solute be a linear function of the applied electric field. Therefore, Z* is not the ionic charge on an interstitial atom, but should be viewed as the number of fundamental charge units that the migrating solute would need in order that its motion in the electric field be guided by the electrostatic force alone. For a two conduction band metal, such as tantalum, there are three distinct contributions to the force F on an impurity. The contribution from the direct external field E acting on the impurity ion is called the electrostatic force
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