Hydrogen Diffusion in Nb-Ta Alloys

G. MATUS[EWICZ and H. K. BIRNBAUM

Gorsky effect measurements of the diffusivity of hydrogen were carried out in Nb-Ta alloys over the entire composition range and over the temperature range 165 K to 500 K. Measurements were made in the solid solution range of hydrogen solubilities and the diffusivities were corrected to zero hydrogen concentration using mean field interaction energies determined from the composition dependence of the diffusivities. Significant deviations from an Arrhenius temperature dependence were observed over the entire composition range. Over most of the temperature range the hydrogen diffusivity exhibited a monotonic decrease as the Ta concentration was increased. The mean field H-H interaction energies also varied with Ta concentration.

I. INTRODUCTION

EXTENSIVE studies of the mobility of H in bcc metals have been carried out using a variety of techniques.~ Long range diffusivity at relatively low temperatures is of particu- lar interest, as it addresses the question of whether the H mobility is dominated by tunneling effects rather than by a classical thermally activated jump process. In these metals reliable low temperature diffusivities have been obtained primarily with the use of the Gorsky effect,1 which has the major advantage of not requiring transfer of the H across the metal surface.

A number of studies of H behavior in the "pure" bcc Group Vb metals has been reported which clearly indicate deviations from a classical Arrhenius temperature de- pendence at temperatures of the order of 250 K. J The reason for this deviation has not been established and indeed is a matter of some dispute. It has been suggested that H mo- ity in the bcc metals is dominated by phonon assisted quan- tum tunneling processes analogous to those observed for small polarons in semiconductorsY In this model, H oc- cupies a set of energy levels at the occupied site which are reduced below those of the adjacent interstitial sites by the "self trapping energy", Eo. Diffusion occurs by a tunneling transition between the occupied and the adjacent energy levels. The form of the H jump frequency depends on whether the tunnel transitions occur between ground states z or via excited state transitions) In the former case, the diffusivity at temperatures above about half the Debye tem- perature, T > 125 K, has the form

D = Do exp - Ea/kT

The Arrhenius form is the high temperature limit of the tunneling behavior and the temperature dependence reflects the self trapping energy rather than the height of the poten- tial barrier. For ground state transitions, deviations from the Arrhenius behavior are expected for T < 125 K.

If transitions between excited states are allowed, 3 devia- tions from the classical Arrhenius behavior are expected at relatively high temperatures, and model calculations suggest a continuous curvature in the log D vs 1/T behavior. An analytic form for this type of behavior is not available, but

it has been suggested 3 that the observed deviation from the Arrhenius behavior at about 250 K results from this high temperature small polaron behavior.

The behavior of the systems Nb-H and Ta-H are of inter- est as these both show significant departures from the clas- sical Arrbenius dependence under certain conditions, 4,s and it is of interest to study the H diffusivity across the Nb-Ta phase diagram. Theoretical treatments of small polaron be- havior are not yet in a form which allows a quantitative description of the variation of H behavior with mass of the host lattice atom. Such a dependence is, however, indicated by the model calculations for excited state transitions 3 and would be reflected through the lattice Debye temperature for the ground state transitions. 2

The Nb-Ta system forms a complete range of solid solutions 6 with no reported ordering or clustering effects and a very small and linear dependence of atomic volume on composition. 7'8 Hydrogen behavior in these solid solutions has been studied by Westlake and Miller s who showed dra- matically increased H solubilities in the Nb-Ta alloys as compared to pure Nb and Ta. A maximum terminal solid solubility in equilibrium with the hydride was observed at a composition Nb03Ta07. Many of the alloy properties which might be related to H mobility, such as the electron density of states, 9 atomic volume, 7 and elastic constants w vary lin- early with alloy composition. In view of this, one might expect a monotonic change of the H diffusion behavior with alloy composition, and this has been observed" at 296 K for compositions between Ta + 25 at. pct Nb and pure Nb. The reported diffusivity ~ for pure Ta is, however, somewhat higher than that for Ta +25 at. pct Nb. The temperature dependence of the diffusivity has not been studied. In the present paper, data will be presented for H diffusion in the Nb-Ta system over the temperature range 165 K to 500 K.

G. MATUSIEWlCZ, formerly with the University of Illinois, is now Research Associa te with Rensse laer Polytechnic Inst i tute . H . K . BIRNBAUM is Professor of Physical Metallurgy, University of Illinois at Urbana-Champaign, Urbana, IL 61801.

Manuscript submitted January 18, 1982.

ISSN 0360-2133/82/1011-1675500.75/0 METALLURGICAL TRANSACTIONS A �9 AMERICAN SOCIETY FOR METALS AND

THE METALLURGICAL SOCIETY OF AIME

II. EXPERIMENTAL PROCEDURES

The H diffusivities were measured using the Gorsky ef- fect, 12 an anelastic relaxation method in which an elastic strain gradient is used to establish a gradient of H concen- tration across the specimen thickness. It has been shown l: that the anelastic relaxation strain, ea, may be described by

~'An ~ ~'OAAn exp ( - t /T ) [1]

where

VOLUME 13A, OCTOBER 1982--1675

and e0 is the elastic strain imposed, Aa, is the anelastic relaxation strength, t is the time, L is the specimen thick- ness, and DM is the hydrogen diffusivity. Higher order terms contribute less than 2 pct to the relaxation strength and have relaxation times so short that to an excellent approxima- tion, the anelastic strain is described by a single experimen- tal relaxation. ~2

In the case of the Nb-Ta alloys, the data were well described by a single exponential relaxation. In order to allow for a distribution of relaxation times, the data at each temperature were fitted with a lognormal distribution of relaxation times ~3 given by the expression

1 ( •An=--"IT - ' ~ exp - ( - - - ~ ) ) exp

- t / r d(lnz) [3]

where ~'m is the most probable relaxation time and/3 is the half width of the Gaussian distribution of relaxation am- plitudes. For all compositions and temperatures studied, the/3 values were less than 1.0 as is consistent with single relaxation behavior. The values of ~-~ obtained by the fitting procedure were used to calculate the diffusivity using Eq. [2].

Specimens having the approximate dimensions 14.0 cm • 0.95 cm • 0.05 cm were elastically strained as canti- lever beams, and the displacement of the end of the speci- men was determined using a capacitor technique to a precision of +5 • 10 -2 micrometers (corresponding to an elastic strain of less than 10-6). The temperature of the specimen was controlled to +0.1 K during the relaxations. Measurements were carried out over the temperature range of 500 K to 165 K with the temperature determined to an accuracy of 0.5 K.

All specimens were given a UHV anneal in the tem- perature range 2200 to 2600 K at vacuums of about 10-Spa resulting in a grain size of the order of 3 • 10- lcm. Vacuum fusion analysis subsequent to these anneals was carried out to establish that the 0 concentration was significantly less than 0.1 at. pct and the N concentration was less than 2 • 10 -3 at. pet. Since the H concentrations used were of the order of 1 to 7 at. pct, the residual interstitial impurities were not considered to be of significance in determining the H diffusivity. The H was introduced by electrolytic charging and its concentration in each specimen determined by both vacuum extraction and from the Gorsky relaxation strength with the two methods giving good agreement to about 10 pct.

I I I . RESULTS AND DISCUSSION

Measurements will be reported for the 25 at. pct Ta- 75 at. pct Nb, 50 at. pct Ta-50 at. pet Nb, 75 at. pct Ta- 25 at. pet Nb alloys as well as for pure Nb. The pure Nb results, which will be discussed in greater detail in a sub- sequent publication, 5 are for specimens which were pre- strained a few pct resulting in diffusivities in excellent agreement with previously published pure Nb data. 4 The data presented for the pure Ta are those of Reference 4.

All of the Group VB metals exhibit a strong dependence of the hydrogen diffusivity on hydrogen concentrations with the diffusivity decreasing as the concentration increases. ~

While a detailed understanding of this effect has not been developed, it appears to result from H-H elastic interactions via the Nb lattice and can be described 4'14'15 in the mean field approximation by

DH =DM 1 -- k T J [4]

where DH is the diffusivity at CH = 0, U is the mean field interaction energy, and k is Boltzman's constant. Values for U can be derived from the concentration dependence of D~ given by Schaumann et al 4 for Nb and Ta and by Peterson and Jensen 1~ for the Nb-Ta alloys using Eq. [4]. These values are given in Table I and have been used to correct the data obtained in the present study to CH - 0.

Table I. Mean Field Interaction Energy

Alloy U (eV/Atom) Reference

Nb 0.21 (1) 75 pct Nb 25 pct Ta 0.11 (11) 50 pct Nb 50 pct Ta 0.16 (11) 25 pct Nb 75 pct Ta 0.16 (11)

Ta 0.17 + 0.02 (4)

A significant variation of U, with a minimum at the Nb rich end of the solid solution range, is observed. This does not correlate with the maximum terminal solid solubility 8 (which occurs at Nbo.3Tao 7) nor with the linear variation of elastic constants ~~ across the phase diagram. This latter ob- servation is somewhat surprising as U is given ~2 (in the mean field approximation) by

2 ( 1 - 2 v ) (A + 2B) 2 U -- Pm [5]

27(1 - v) K

where v is Poissons ratio, Pm the critical concentration of the a - a ' miscibility gap, (A + 2B) is the trace of the di- pole tensor which describes the distortion field around the H solute, and K is the bulk modulus.

The variation of Dn with temperature is shown in Fig- ure 1. All of the alloys exhibited non-Arrhenius temperature dependences of the diffusivities over the temperature range examined, with the data being best fit by continuous curves. Over most of the temperature range, the magnitude of Dn decreases as the Ta concentration increases except at the lowest temperatures where the much more pronounced non- Arrhenius behavior in pure Ta results in a higher diffusivity of H in pure Ta than in the alloys. The present data for Nb are in excellent agreement with that reported by Schaumann et al 4 (although agreement required a small plastic de- formation of our specimensS). The DH values for the Nb-Ta alloys at 296 K are in reasonable agreement with those of Peterson and Jensen. ~

Deviations of DH from an Arrhenius temperature de- pendence are observed for all compositions in the Nb-Ta system. The mechanism causing the behavior is not estab- lished and remains somewhat controversial. Since the alloys are random solid solutions, the departure from a classical temperature dependence clearly occurs in the presence of a random variation in lattice potential. In the small polaron theories this corresponds to a spatial variation of the self trapping energy and the transition matrix element. While

1676--VOLUME 13A, OCTOBER 1982 METALLURGICAL TRANSACTIONS A

_42,00 100 0 I

- 5 0 I

Nb

- I00 ~

[] 25% To

o 50% To

a 75% To

IM

E CD

v

1:::3

{ D o _J

- 6

- - - - To (Ref. 4)

x ~

\

-7 L ~ t ~ L J ~ ~ ~ ~ J 2 $ 4 5 6 7

IO00/T(K) Fig. 1 - - Hydrogen diffusivity in Nb-Ta alloys as a function of temperature. The data were corrected to Cr~ = 0 using a mean field correction.--Pure Nb (subjected to a 10 pct plastic strain before measurement; Ref. 5). . . . . Pure Ta (data from Ref. 4). D 25 pct Ta, 75 pct Nb. O 50 pct Ta, 50 pct Nb. A 75 pct Ta, 25 pct Nb.

this spatial variation may still allow a hopping type of tun- neling between interstitial sites, it certainly destroys any coherence in the tunneling process. The metal-H and H-H interactions differ significantly for the Nb and Ta systems as may be seen most graphically by the differences in their phase diagrams. 16 Thus, the operative diffusion mechanism which accounts for the non-Arrhenius behavior must allow for the spatial variation of these interaction energies in the alloys.

As is evident from Figure 2, the variation of DH with alloy content is monotonic but nonlinear, particularly at the lowest temperatures. No evidence for the minimum in DH reported by Peterson and Jensen I~ at 296 K is seen in the present data. Their value for DH in pure Ta is, however, higher than that reported by Schaumann e t a l 4 and used in the present dis- cussion. The greatest dependence on composition appears to be in the temperature dependence of the diffusivity, which, however, is difficult to quantify because of the non- Arrhenius behavior. It is not possible to relate this de- pendence to the parameters of the small polaron theory of diffusion, as this is not yet available in a suitable ana- lytic form.

IV. CONCLUSIONS

Hydrogen diffusivity in Nb-Ta alloys exhibited a mono- tonic decrease with increasing Ta concentration over the

- I 0

"-d\~ -12 o

E -15 "I- .

121 /

-Iz

-16 I I , I I i I I , I 0 0.2 0.4 0.6 0.8 1.0

Atom Froclion Nb Fig. 2--Variation of the hydrogen diffusivity with composition across the Nb-Ta solid solution range.

temperature range 500 K to 190 K. Below 190 K the non- Arrhenius temperature dependence caused the H diffusivi- ties in pure Ta to exceed those of alloys containing some Nb.

All of the alloys exhibited a non-Arrhenius temperature dependence with the deviation from a classical temperature dependence being greatest for pure Ta.

The mean field H-H interaction energy exhibited a marked decrease on adding Ta to Nb with a minimum value of 0.11 eV per atom at a composition 75 at. pct Na 25 at. pct Ta.

ACKNOWLEDGMENTS

The authors would like to acknowledge gratefully the assistance of Professor D.T. Peterson of Iowa State Uni- versity who provided the Nb-Ta alloys. This work was sup- ported by the Department of Energy Contract DOE-EY-C- 02-1198.

R E F E R E N C E S

1. J. V61kl and G. Alefeld: Hydrogen in Metals, Springer Verlag, Berlin, G. Alefeld and J. V61kl, eds., 1978, vol. 1, pp. 321-48.

2. C.P. Flynn and A.M. Stoneham: Phys. Rev. B, 1970, vol. 1, pp. 3966-78.

3. D. Emin, MI. Baskes, and W.D. Wilson: Phys. Rev. Let., 1979, vol. 42, pp. 791-94.

METALLURGICAL TRANSACTIONS A VOLUME 13A, OCTOBER 1982-- 1677

4. G. Schaumarm, J. V61kl, and G. Alefeld: Phys. Stat. Sol., 1970, vol. 42, pp. 401-t3.

5. G. Matusiewicz and H. K. Birnbaum: Univ. of Illinois, Urbana, IL, unpublished research, 1981.

6. R.P. Elliott: Constitution of Binary Alloys, First Suppl.. McGraw- Hill, New York, NY, 1965, p. 272.

7. D.G. Westlake: Scripta Met., 1977, vol. 11, pp. 689-92. 8. D.G. Westlake and J. E Miller: J. Less Common Met., 1979, vol. 65,

pp. 139-54. 9. J.M. Corsan and A.E Cook: Phys. Stat. Sol., 1970, vol. 40,

pp. 657-65. 10. E.S. Fisher, J. E Miller, H. L. Alberto, and D. G. Westlake: J. Phys.

F: MetalPhys., 1981, vol. 11, pp. 1557-76.

11. D.T. Peterson and C.L. Jensen: MetalL Trans. A, 1980, vol. I1A, pp. 627-31.

12. J. V61kl, G. Schaumann, and G. Alefeld: J. Phys. Chem. Sol., 1970, vol. 31, pp. 1805-09.

13. A.S. Nowick and B.S. Berry: I .B.M. Journal, 1961, vol. 5, pp. 297-320.

14. H.C. Bauer, J. Vflkl, J. Tretkowski, and G. Alefeld: Z. Physik, 1978, vol. B29, pp. 17-26.

15. H. Wagner: Hydrogen in Metals, Springer Verlag, Berlin, G. Alefeld and J. V61kl, eds., 1978, vol. 1, pp. 5-52.

16. T. Schober: Hydrogen in Metals, Springer Verlag, Berlin, G. Alefetd and J. V61kl, eds., 1978, vol. 2, pp. 11-72.

1678--VOLUME 13A, OCTOBER 1982 METALLURGICAL TRANSACTIONS A