Hydrogen permeation and diffusion in niobium
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I.
dp= D S
INTRODUCTION
HYDROGEN transport in Group Vb metals, such as niobium, has been a subject of extensive scientific and technological interest. Below 573 K, hydrogen diffusion has been studied by surface-independent methods such as the Gorsky Effect, and the diffusivity is characterized by a value of D ~ 5 x 10 -9 m 2 per second at 300 K and a low activation enthalpy of about 10.3 M/mole H (0.11 ev per atom). Non-Arrhenius behavior has been observed below room temperature where a decrease in activation energy has been reported, 1 but its cause is a matter of some dispute. A nonclassical isotope effect has been observed 1'2 at low temperatures such that hydrogen and deuterium diffusion constants display different activation enthalpies and the ratio of the isotopic diffusivities deviates markedly from the inverse square root mass dependence. The Gorsky Effect suffers from hydrogen evolution from the specimen above about 573 K, and surface-dependent methods such as permeation, 3'4 absorption, s desorption, 6 and hardness 7 have been applied to measure hydrogen transport at elevated temperatures. These techniques can be strongly affected by the possible influences of a surface barrier in a reactive metal such as niobium and generally have resulted in data exhibiting large scatter and poor agreement. In the present experiments we performed gaseous permeation experiments to measure the high temperature permeability and diffusivity of hydrogen and deuterium in niobium, taking particular care to minimize surface barriers. We will describe the method of permeation and procedures used to measure the hydrogen flux. We will also discuss the permeability and diffusivity results for hydrogen and deuterium in relation to the values obtained at low temperatures.
II.
THEORY OF THE METHOD
Under conditions where diffusion of hydrogen atoms in the lattice is the rate limiting step, the permeation constant, 9 , is defined as the product of the diffusion constant, D, and the solubility constant, S: 8 ROBERT SHERMAN, formerly with the University of Illinois, Urbana, IL, is now with Southwest Research Institute, San Antonio, TX 78284. H.K. BIRNBAUM is Professor of Physical Metallurgy, University of Illinois, Urbana, IL 61801. Manuscript submitted March 25, 1982. METALLURGICALTRANSACTIONS A
[1]
The above quantities can be expressed in an Arrhenius form as: - ~0 exp - AH./RT
AHo/RT
O = D0 exp -
S = So exp - AHs/RT
[2a]
[2b] [2c]
From the above, we find that AH. = AHo + AHs ~o = OoSo
[3a] [3b]
From previous measurements of the hydrogen diffusivity~ and solubility,9 we find the expected permeation constant for hydrogen to be ~
(torr-liters/cm-sec- t ~ )
= 1.35 x 10-5 exp 9 25.1 M/mole H/RT
and for deuterium qbc~ (torr-liters/cm-sec-tVmff)= 1.43 x 10-5 exp 9 22.9 M/mole DIRT
[41 The units used for ~ were the traditional units of torr-liters/ cm-sec- tVi-o-ff. The corresponding SI units are 8.67 x 10 .4 Pa-dm3/m-sec-X/~. The same hydrogen solubility constant, extrapolated to low concentrations, ~~was used both for hyd
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