Thermotransport of Hydrogen and Deuterium in Vanadium, Niobium, and Tantalum
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I.
the logarithmic solute concentration gradient,
INTRODUCTION
A temperature gradient in a material may cause concentration gradients to develop due to thermotransport or thermigration. Thermotransport phenomena are poorly understood at present and additional data are needed on the fundamental behavior of solutes in metals. A redistribution of solutes by thermotransport may be undesirable in some engineering application of metals. The transport behavior of hydrogen in the Group V B transition metals is of particular interest because hydrogen can severely degrade the mechanical properties of these bcc refractory metals.l'2 Existing atomistic models for thermotransport cannot predict the direction or magnitude of thermotransport in any given metal-solute system. Efforts to evaluate critically plausible mechanisms and driving forces for thermotransport have been hindered by a shortage of experimental data. Among the questions needing further study are isotope effects and temperature dependence of the heat of transport. Isotope effects have been reported 3'4'5 for thermotransport of hydrogen and deuterium in niobium (columbium), iron, nickel, and zircaloy-2. However, an isotope effect was clearly established only in the case of nickel because in the other metals the observed differences were less than the total uncertainty in the measurements. The heat of transport, Q *, arises from a phenomenological treatment of thermotransport. 6-9 It has the dimensions of energy, and considerable effort has been expended to produce an atomistic interpretation of this energy. 4'9-13 Whether Q* is temperature dependent would seem relevant to such interpretation. A temperature dependence for Q* has been reported for hydrogen in iron, 4 nickel, 4 and/3-zirconium, 14as well as for oxygen in tantalum.15 The present study of thermotransport of hydrogen and deuterium in Group V B metals was undertaken to measure Q*, to look at isotope effects, and to investigate the temperature dependence of Q *. Solute migration during thermotransport may be viewed as atomic movement due to applied forces. For a onedimensional geometry, the force components 11'12arise from D.T. PETERSON is Professor, Department of Materials Science and Engineering, Iowa State University, and is Senior Metallurgist, Ames Laboratory-USDOE, Ames, IA 50011. M. E SMITH, formerly Graduate Student, Department of Materials Science and Engineering, Iowa State University, is now with Sandia Laboratories, Albuquerque, NM 87115. Manuscript submitted April 10, 1981. METALLURGICAL TRANSACTIONS A
Fc = - R T (d In C /dx)
[1]
and the logarithmic temperature gradient, Fr = - a * (d In T/dx)
[2]
where R is the gas constant and x is a space coordinate. It is evident that Q* has dimensions of energy and the sign and magnitude of Q* characterize the direction and scale of thermotransport. A steady state technique was employed in the present investigation. At steady state, the sum of the two force components, Fc and Fr, is zero so that Eqs. [1] and [2] can be combined to obtain the foll
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