hydrogen permeation and diffusion in niobium

Hydrogen Permeation and Diffusion in Niobium

ROBERT SHERMAN and H. K. BIRNBAUM

High temperature hydrogen permeation experiments were performed on niobium using ultra high vacuum techniques in an attempt to maintain clean specimen surfaces. Diffusivities and permeabilities were measured from 700 K to about 1400 K at hydrogen pressures ranging from 4.26 Pa to about 0.013 Pa. The measured diffusivities are in agreement with values extrapolated from the low temperature surface independent measurements. In contrast to low temperature measurements, a trend indicating a classical isotope effect is observed for hydrogen and deuterium diffusivities in niobium at the higher temperatures. The measured hydrogen permeation constants agree with independent solubility and diffusivity measurements and are characterized by a negative enthalpy, as expected from low temperature solubility and diffusivity measurements. These results are contrasted with previous measurements which appear to have been controlled by surface reactions.

I. 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.

dp= D S [1]

The above quantities can be expressed in an Arrhenius form as:

- ~0 exp - AH./RT [2a]

O = D0 exp - AHo/RT [2b]

S = So exp - AHs/RT [2c]

From the above, we find that

AH. = AHo + AHs [3a]

~o = OoSo [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 hydrogen and deuterium in arriving at Eq. [4]. Since the enthalpy of permeation is negative (due to the large exothermic heat of solution), the quantity of hydrogen permeating the sample at a constant input pressure will decrease as the temperature is increased. Figure 1 shows this calculated permeation constant for hydrogen along with previous experimental measurements.

In the present experiments, the total hydrogen flux, f, across the cylindrical sample of length h was measured by monitoring the pressure drop across a known conductivity. At steady state, the flow of hydrogen through the niobium specimen (f) equals the flow through the conductance to the pump and is given by

f = CL(P~ - P2) [5]

ISSN 0360-2133/83/0211-0203500.75/0 �9 1983 AMERICAN SOCIETY FOR METALS AND

THE METALLURGICAL SOCIETY OF AIME METALLURGICAL TRANSACTIONS A VOLUME 14A, FEBRUARY 1983--203

-2 I 0 0 0 6 0 0 4 0 0 C I0 ~ I , I , ,

16'

i o,

i d 8

I I i

r -

I t I I I 0.8 1.0 1.2 1.4 1.6 1.8

10:5/T (K) -I

Fig. l - - Comparison of the calculated hydrogen permeation constant and previous hydrogen permeation experiments. �9 Reference 4, O Reference 3.

where PI is the pressure at the niobium sample exit surface and P2 is the pressure behind the conductance at the pump. From Fick's first Law we can state u that at steady state the total flux of hydrogen through a cylindrical sample is

f _ 27rh @(%/~o- v~P-~) [6] In b/a

and with Eq. [5], we find

In b/a CL(Pl -- P2) = 2--~ V'-P0 - %/'-ill [7]

where b and a are the outer and inner radii, respectively, and P0 is the hydrogen input pressure at the entrance surface r = b.

Figure 2 shows the time dependence of the flux; as seen, it is characterized by a steady state behavior at long times and an initial transient. The diffusivity may be determined from the time dependence of this transient behavior which is obtained by solving Fick's second Law with the following boundary conditions:

t = 0 C = 0 for a < r < - b

t > O C= Co at r = b

C = 0 at r = a

Using the solution given by Crank, ~2 the flux can be found by evaluating the spatial gradient at the exit surface, r = a:

/

I II f

71

- . . . / / I

Flux

tb fi Time

Fig. 2 - -The time dependence of the uptake flux showing the 2 characteristic times. The breakthrough time is tb, and t~ is the inflection time.

1 2 Jo(aa,)Jo(ba,) f = 27rhdP V~o ~ + 2 JZo(-~a,) ~ ~-~'ban)

n=l

exp - DaZ, t} [8] I

where,/0 is a Bessel function of first kind of zeroth order and a. is the eigenvalue. Two times, the inflection time ti (the time to the point of inflection) and the breakthrough time to (the intersection with the time axis of the tangent line at ti), have been related to the diffusivity in planar geometry: 13

d 2 In 16 ti = 3,rrZD [9a]

0.Sd 2 tb ~rZD [9b]

where d = b - a is the wall thickness. For cylindrical geometry, it has been shown 14 that the expressions for the inflection and breakthrough times can be approxi- mated by using the planar expressions for these two characteristic times.

I I I . E X P E R I M E N T A L M E T H O D

Niobium samples, having the form shown in Figure 3 and the dimensions given in Table I, were machined from 2.5 cm OD polycrystalline rods. Samples were annealed in a UHV furnace at a vacuum of about 10 -7 Pa at 2400 K for 24 hours yielding a grain size of greater than 1 cm and relatively high purity particularly with respect to interstitial impurities. After the UHV anneal, the specimens were elec- tron beam welded to the molybdenum tube assembly. Chemical analyses (see Table II) were carried out after all of the experimental runs were completed since the specimen shape precluded analyses without cutting the specimen. Spark source mass spectroscopy was used for substitutional

204--VOLUME 14A, FEBRUARY 1983 METALLURGICAL TRANSACTIONS A

Molybdenum tube

Iolybdenum tube

Table II. Specimen Purity

Substitutional Impurities* (Atomic ppm)

W Fe Cr Si Ta Ni Ca A1

2 2 2 3 10 1 2 1

Interstitial Impurities (Atomic ppm)

Sample Number C O N

1 95 520 135 2 230 66 73

*All other elements are undetected.

The sample insert was placed into a UHV permeation sys- tem with a base pressure of 9 x 10 -8 Pa (6 • 10 -1~ torr), shown schematically in Figure 4. The sample was centered in a 0.25 mm thoriated tungsten wire resistance furnace. Three W-25 Rh/W-5 Rh thermocouples monitored the temperature of the sample. During a run, the sample temperature was maintained to within - 3 K, but a temperature gradient of about 3 pct of the median temperature existed along the length of the niobium sample.

The input hydrogen gas was purified by diffusion through a Pd-Ag membrane cell, and the input pressure was adjusted by an automatic pressure regulator used in conjunction with

.J L

iobium sample

Fig. 3'--The niobium sample insert. The symbols are defined in Table 1.

Table I. Sample Dimensions (cm)

Wall Sample Total Sample Thickness O.D. Length Length Number d 2b h l

1 0.318 2.46 5.72 7.23 2 0.483 2.49 5.97 7.76

elements, and vacuum fusion was used for O, C, and N interstitials. Based on previous experience in our laboratory, as well as results in the literature, 1~ we estimate that the substitutional solute concentrations did not change as a re- sult of exposure to the vacuum and hydrogen environments during the experimental runs, but that the interstitial impurity concentrations increased.

C

M

i

i m ii

�9 l K Po

Fig. 4 - The experimental arrangement for hydrogen permeation studies. A, sample insert; B, isolation valve; C, gauge for pressure P~; D, known conductance; E, gauge for pressure P2; F, getter pump (SAES); G, He cryopump; H, hydrogen purification and automatic pressure regulator valve; I, furnace; J, gauge for pressure Po; K, temperature controller; L, thermocouple feedthrough; and M, mass spectrometer.

METALLURGICAL TRANSACTIONS A VOLUME 14A, FEBRUARY 1983--205

I000 800 600C dynamic pumping by the cryo-sorption pumps or the helium cryopump. Since both these pumps had a much greater pumping speed for other gases than H2, this procedure served to maintain impurity levels in the H2 gas as low as possible. The composition of the gaseous atmosphere was monitored by a mass spectrometer. At H2 input pressures below 0.13 Pa the cryopump maintained the gaseous impurity levels at about 0.003 of the H2 pressure, while for Hz pressures greater than 0.13 Pa, we estimated the impurity levels to be about 0.02 of the Hz pressure. The major source of gaseous impurities was the dissociation of the H2 molecules by the hot furnace filaments and the reaction of the atomic H thus produced with the oxides on the stainless steel vacuum chambers. 16 This produced a background H20 partial pressure which, while reduced by the cryopump, served as the major gaseous contaminant. The increase of H20 partial pressure with time when the hot filaments were on could be directly observed.

A known conductance separated the two volumes in which pressures P~ and P2 were measured by ion gauges operated under conditions which minimized gauge pumping. The volume in which P2 was measured was pumped by a SAES Zr-A1 getter pump which served to remove hydrogen gas reversibly at room temperature.

For measurements at temperatures above 1200 K, the sample was heated until stabilization of pressures and temperatures occurred. For measurements at temperatures below 1200 K, the sample would first be annealed above 1200 K for about 20 minutes, and then the temperature would be lowered to the desired setting. About 20 minutes was allowed for stabilizing the pressure and temperature.

IV. RESULTS AND DISCUSSION

A. Permeation of Hydrogen

Our steady state pressures were related to the flux of hydrogen molecules, using Eq. [5]. The pressure gauge readings were corrected for the differences in the ionization probabilities of H2 and of N2 as the gauges were calibrated for the latter gas. All the gauges were calibrated against each other, and the appropriate correction factors were used. For some measurements, such as P0 and the data given in Figure 7, it was necessary to know the pressures at the specimen surface at the temperature of measurement. The gauge readings were corrected for transpiration using 17

pCOrr = 2 pm . . . . ( 2 7 3 ) \ -~R / " {1 - fl(1 - ~ ) } [10]

where Tv is the temperature at the point of interest, TR is room temperature, and fl is the volume fraction of the sys- tem at temperature TF. The factor of 2 converts the gauge readings to hydrogen pressure since they were calibrated for N2 gas.

Figure 5 and Table III show the hydrogen permeation data for samples at several different pressures. While the data were obtained over a very wide temperature range, surface impedance effects were clearly evident at the lower temperatures, and the data are not included in Figure 5 or in the analysis leading to the parameters of Table III. The criterion for inclusion of the low temperature data points in

16 3

8

~ 6

0

E 4

O~

16 4

I0-3

I I I I /

-- ~ 0 0 O ~ j v o 3

I J I 0 .8 1.0 1.2

103/m (K -~) (a)

I000 800 600C

H - ~'CALC

[ I I H

8 - cI)c A LC I

2

I I I I I I 1(5 .7 0.8 0.9 1.0 I.I 1.2 1.5 1.4

105/T (K -I )

(b) Fig. 5--Permeation data for (a) sample #1 and for (b) sample #2. Symbols and statistical fitting parameters are given in Table III. The permeability calculated from Eq. [4] is also shown for comparison. The error estimated from an analysis of the experimental variables is shown.

the analysis is that the included point be within one standard deviation of the extrapolated permeation value obtained from the least squares fit of the higher temperature points. The lower temperature points will be discussed later. The high temperature data exhibited the expected negative enthalpy of permeation (Eq. [4]) with values ranging from 10 to 31 kJ/mole H for each individual run. For reasons which will be discussed subsequently, the most reliable data are considered to come from the first runs for each specimen.

The average values of the permeability for all runs is

(qb H) = 4 • 10 -5 exp 20.7 kJ/mole H/RT [11]

while for the most reliable first runs from both samples

(@"> = 1.6 • 10 -5 exp 30.6 U/mole H/RT [12]


Table III. Permeation Data

Series poH2(pa)

Sample Number 1 (Figure 5(a))

Temperature Range Symbol of Fit (K) AH~,(kJ/mole H) In ~o

I 0.50 3 0.19 4 0.047 6 0.48

1 0.047 3 0.017

O 820to 1300 -30.1 --- 3.7 -10.7 --- 0.4 /k 910to 13130 -16.1 - 3.2 - 9.4 - 0.4 V 910 to 1250 - 9.8 --- 7.5 - 8.9 +-- 0.9 �9 1030 to 1310 -15.1 --- 5.4 - 9.4 --- 0.5

Sample Number 3 (Figure 5(b))

O 920to 1350 -31.0 --- 6.6 -11.4 --- 0.7 �9 140 to 1400 -22.3 - 7.2 -10.9 • 0.6

These values were obtained by averaging the enthalpies and preexponential values from Table III. We did not perform a least squares analysis on the total set of data points since there is a nonrandom error in the data due to changing impurity levels from sample to sample and for each series of runs. The discussion of the effect of impurities on a possible surface barrier follows. These values may be compared to those expected from the low temperature diffusivity and solubility results as given in Eq. [4], and the agreement is seen to be quite good.

The experimental results clearly showed the effects of surface impedances on the permeation of hydrogen even at temperatures as high as about 1000 K. These were mani- fested in several ways. A marked deviation from the classical behavior was observed at each pressure of H2 as the temperature was decreased (Figure 6). Even on the first runs for each specimen, the low temperature data consistently fell below the values extrapolated from the high temperature points, gradually achieving a positive "effective enthalpy" of permeation at the lower temperatures. The effect was reversible, however, in that the high temperature points could be reproduced (within the experimental error) after the low temperature points were established. As seen in Figure 6, repeated measurements on the same specimen resulted in an increase in the temperature at which the marked deviation from the high temperature behavior was observed. This behavior also accounts for the decrease in the effective enthalpy with repeated measurements (Table III) since, as the experimental maximum in qb moves toward higher temperatures, the effective AH measured at temperatures near 1000 K will decrease. Also shown in Figure 6 is a set of measurements taken at PH~ = 4.3 Pa (0.032 torr) which exhibits a positive AH over the entire temperature range. Apparently at this relatively high pressure the surface impedance effects extend over the entire temperature range examined. This form of behavior is consistent with the development of a surface permeation barrier which leads to entrance or exit surface controlled permeation.

Such surface barriers may be due to the formation of a surface oxide despite the UHV conditions of the experiment. Two sources of oxygen for the formation of such an oxide are present: internal solute O which segregates to the surface and reactions in the nominally high purity H2 atmosphere. Both appear to have occurred.

Surface O coverage, and possibly oxide formation, can occur by segregation from the solid solution to the external surface. Such equilibrium segregation of bulk oxygen to the surface of niobium has been observed, ~s and it has been

16 3

>,

~5 5

E

ta

16 4

I l I

-- O ~

I I t o.8 1.o 1.2 1.4

103/T (K -I)

Fig. 6 - -Pe rmea t ion data showing the time dependence of the low temperature points for sample #1 . The symbols correspond to those of Table III. The runs were made in the order in which the series are num- bered. The squares are for the second series of runs on sample # 1 at an input hydrogen pressure of 4.3 Pa. The lines indicate general trends rather than a fit to the data.

shown that such an overlayer can lead to a permeation barrier at lower temperatures. ~9 This surface barrier, and its disappearance at high temperatures, is consistent with previous tritium evolution experiments 2~ and is consistent with the present observations of permeation behavior at higher temperature. Surface barriers formed by equilibrium segregation from the solid solution occur at increasingly higher temperatures as the O concentration in the solid solution increases. In the present experiments this is evidenced by a decrease in the low temperature permeability with time as shown by the sequence of measurements in Figure 6.

Support for the increase in oxygen concentration with exposure to the H2 gaseous atmosphere comes from the interstitial analyses (Table II) performed after completion of the permeation measurements. Sample #1 contained more oxygen than sample # 2 and was subjected to a greater exposure to H2 gas and to higher hydrogen pressures than sample #2. Since both specimens received similar purification treatments, this change in oxygen concentration is taken as evidence for oxygen uptake in our sample and supports the suggestion of the formation of surface barriers at lower temperatures.

In view of the evidence for the formation of surface barriers at low temperatures, it is necessary to demonstrate that there was no surface impedance at the higher temperatures where the data were used for Eqs. [11] and [12]. For


diffusion controlled permeation, Eq._[6] predicts a linear relation of the steady state flux vs (V'-ffo - V'-fi~) at a given temperature. Figure 7 shows that at the higher temperatures, this condition is satisfied. Another condition for diffusion controlled permeation (Eq. [6]) is a linear relation between the steady state flux and the geometric factor 27rh/In (b/a) at constant temperature and input pressure. Figure 8 shows reasonable agreement with the expected linear relationship for the two specimen geometries used.

B. Hydrogen Diffusivity

Analysis of the initial transients of the hydrogen flux after a pressure increment yields the H diffusivity as discussed in Section II. (There is a correction to the transient flux due to gas buildup in the volume in which the pressure Pl is measured. This term, V1/RT(dP1/dt) was at most 1 pct of the flux and was ignored in our analysis.) In the present experiments the flux was measured directly and the diffusivities were obtained using Eqs. [8] or [9]. The data were fitted to the first three terms of Eq. [8] using D as a fitting parameter in a linear regression analysis. The results of this analysis and that obtained by measurements of the breakthrough time (Eq. [9]) were in agreement to within the experimental error.

The analysis of the transient behavior to obtain diffusivities is subject to error due to surface impedances and trapping in the volume of the specimen. As discussed previously, surface impedances affect the behavior only below about 1100 K and should not be significant above that temperature. It is not expected that bulk trapping effects are significant above 1000 K for the concentrations of traps (Table II) present in the specimens and the binding enthalpies characteristic of these traps ( -10 kJ/mole). 2~ The diffusivities obtained from the transient analyses

x I0 3

tO

tt)

tt)

I

4.0 I I I I

~ o 3.0 / n

I I i ' x l . x

9. . I . . I

i2," . P / i.o ./." J,-{,r

, , 1.0 2.0 5.0 4.0

v/'~O - # (Po) I/2

Fig. 7 - - T h e steady state flux plotted against N/fro - V'ffl showing bulk control for the given temperatures. Data for sample # 1 are shown. The error estimated from the experimental variables is shown. 0 - - - 1293K, - - - - - - O . . . . 1253K, - - . . • and

[ ] 1143 K.

6

o • 5 to o t~

) 4

I ~ 3

7

I

2 S >/- 5O

shown . . . . . [ ] . . . . - a - - - - - - 1143 K.

O _

/

I I00

2rrhlln bla (cm)

Fig. 8 i p l o t of the steady state f lux vs the geometr ic factor (2zrh/In (b/a)). The error estimated from the experimental variables is

1253 K, - - . - - O - - . - - 1213 K, and

(Figure 9) are consistent with these conclusions. At temperatures above about 1100 K, the data agree well with that extrapolated from the low temperature data of Schaumann et al I and Matusiewicz. 2 The Arrhenius relation for hydrogen diffusion is

DH(m2/s) = 4.4 -- 0.6 x 10 -8 exp -- 12.8

• 1.1 kJ/mole H/RT [13]

Below about 1100 K, the diffusivities decrease below the low temperature extrapolated values as expected from the formation of surface barriers and from bulk trapping (Figure 9). An Arrhenius relation fitted to the low temperature points is characterized by an activation enthalpy of 38.6 kJ/mole H (0.4 eV/atom) similar to that measured by Albrecht. 5 Based on the available data, it is not possible to determine whether the lower temperature diffusion is controlled by trapping or surface impedances.

C. Isotope Effect

The isotope effect on permeation and diffusion was determined using deuterium gas and the procedures previously described. The deuterium permeation data averaged over both samples was

(~D) = 2.6 X 10 -5 exp 33.1 kJ/mole D/RT [14]

Using the transient analysis, the deuterium diffusivity at T > 1100 K was determined to be

DD(m2/sec) = 3.1 --- 0.5 x 10 -8 exp - 14.0

• 1.1 (kJ/mole D)/RT

On comparing this expression to Eq. [13] it is seen that the enthalpies for hydrogen and deuterium diffusivities are


2

"~ i d 4 Od

E 8

"s 6

4

id

I 0 0 0 8 0 0 6 0 0 5 0 0 C I I I I

~ " " " " " "~" " " "-- -.... R e f I

o " ~ . ~ Ref 2

I I I 0 . 8 1.0 1.2 1.4

1 0 3 / T (K -])

Fig. 9--Diffusion data plotted vs inverse temperature. The errors estimated from the experimental variables are shown. C) sample #1 0.50 Pa H2, �9 sample #2 0.047 Pa Hz and 0.017 Pa H2, and [] sample #1 0.048 Pa Dz.

equal to within the experimental errors, and the Do values are in the approximate ratio DH/D~ ~ V~ as expected from a classical isotope effect.

In order to examine further the isotope effects, the ratios of diffusivities (measured by transient effects) and permeabilities were measured by making alternating series of measurements using hydrogen and deuterium. The diffusivities were determined at a pressure of 0.48 Pa and the permeabilities were measured at a pressure of 0.053 Pa. The ratios, shown in Tables IV and V, have the values

(DH/D D) = 1.46 --- O. 12

((I)"/(I) ~ = 1.48 -+ 0.23

The results indicate that the high temperature isotope effect for diffusivity and permeability are close to the expected classical ratio.

V. CONCLUSIONS

High temperature hydrogen permeation measurements were carried out in high purity niobium at low H2 pressures and in the temperature range 700 to 1400 K. The steady state permeability at T > 900 K was in good agreement with that calculated from low temperature diffusivity and solubility measurements. It can be described by

H 2 qb (torr-liters/cm-sec- tX/m~o~) =

1.6 • 10 -5 exp 30.6 M/mole H/RT

At temperatures below about 1000 K there is evidence for a surface impedance, and the data exhibit a decreasing

Table IV. Isotope Effect for Diffusion

T ~ DH/D D Du/DD

1020 1.56 1.31 980 1.59 1.33 938 1.55 1.36 870 1.58 1.40

{DH/D D) = 1.46 +- 0.12

Table V. Isotope Effect for Permeation

1020 1.3 980 1.6 940 1.9 870 1.4 840 1.3 760 1.4

(dPH/q~ D) = 1.48 --- 0.23

with decreasing temperature in contrast to the volume controlled high temperature permeability.

Measurements of the permeation transients lead to diffusivities which are in agreement with values extrapolated from low temperature Gorsky Effect measurements and may be described by

D H (m2/sec) = 4.4 x 10 -8 exp - 12.8 kJ/mole H/RT

at T > 1100 K. At lower temperatures the DH values decrease below those given by this expression due to the development of surface impedances.

Measurements of the isotope dependence of the diffusivity and permeability indicate a classical mass dependence within experimental error for hydrogen and deuterium at high temperature.

ACKNOWLEDGMENT

Research was supported by the Department of Energy, under contract DE-AC02-76ER01198.

REFERENCES

1. J. Volld and G. Alefeld: Hydrogen in Metals, G. Alefeld and J. Volkl, eds., Springer-Verlag, New York, NY, 1978, vol. 1, p. 321.

2. G. Matusiewicz and H.K. Bimbaum: J. Phy. F: Metal Phy., 1977, vol. 7, p. 2285.

3. E.A. Steigerwald: NASA CR-54004, ER-5623, 1963. 4. D.W. Rudd, D.W. Vose, and S. Johnson: J. Phy. Chem., 1962,

vol. 66, p. 351. 5. W.M. Albrecht, W.D. Goode, and M.W. Mallet: J. Electrochem.

Soc., 1959, vol. 106, p. 981. 6. L. Ryabchikov: Ukrains'kyj Fiz. Zhu., 1964, vol. 9, p. 293. 7. T. Ogurtani: MetalL Trans., 1971, vol. 2, p. 3035. 8. W.M. Robertson: Z. MetaUk., 1973, vol. 64, p. 436. 9. E. Veleckis and R.K. Edwards: J. Phys. Chem., 1969, vol. 73,

p. 683. 10. R. Stickney: The Chemistry of Fusion Technology, D.M. Gruen, ed.,

Plenum, New York, NY, 1972, p. 241. 11. O.D. Gonzalez: Trans. TMS-AIME, 1969, vol. 245, p. 607.


12. J. Crank: The Mathematics of Diffusion, Oxford, 1975, p. 84. 13. N. Boes and H. Zuchner: J. Less-Com. Metals, 1976, vol. 49, p. 223. 14. R. Sherman and H. K. Bimbaum: Metall. Trans. A, 1982, vol. 13A,

p. 174. 15. K.K. Schulze: J. of Metals, 1981, vol. 33, no. 5, p. 33. 16. L.C. Beavis: J. Vac. Sci. Tech., 1973, vol. 10, p. 386. 17. W. Rodgers, R. S. Buritz, and D. Alpers: J. Appl. Phy., 1954, vol. 25,

p. 868.

18. S. Hoffman, G. Blank, and H. Schultz: Z. Metall., 1976, vol. 67, p. 189.

19. R. Sherman and H.K. Birnbaum: unpublished research, Univ. of Illinois, Urbana, IL, 1982.

20. D. Chandra, T. S. Elleman, and K. Verghese: J. Nucl. Matt., 1976, vol. 59, p. 263.

21. C.A. Wert: Hydrogen in Metals, G. Alefeld and J. Volkl, eds., Springer-Verlag, New York, NY, 1978, vol. II, p. 305.


hydrogen permeation and diffusion in niobium

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