Hydrogen diffusion in V-Ti solutions

Scripta METALLURGICA

Vol. 21, pp. 1263-1265, 1987 Printed in the U.S.A.

Pergamon Journals, Ltd. All rights reserved

HYDROGEN DIFFUSION IN V-Ti SOLUTIONS Rex B. McLellan Department of Mechanical Engineering and Materials Science William Marsh Rlce University Houston, Texas 77251 (Received J u l y 13, 1987)

In recent work on the d i f f u s i v i t y of hydrogen in V-Ti solid solutions containing up to 30 At.% Ti in the temperature range 230-473 K, Peterson and Herro [1] have concluded that their data are not in accord with a simple trapping model given by Kirchheim [ 2 ] . The theoretical d i f f u s i v i t y may be written, = [ i + CO exp(-G/kT)] " I

(i)

where I is the d i f f u s i v i t y ratio ( i . e . ratio of the d i f f u s i v i t i e s in the ternary to the binary H-metal solutions), CO is the fraction of i n t e r s t i t i a l sites which are "trap" sites, and G is a trapping free energy. Eqn. ( I ) has also been given previously in essentially the same form by Oriani [3] and Koiwa [ 4 ] . The purpose of the present note is to point out that the conclusion reached by Peterson and Herro [ I ] in respect to the model underlying eqn. (1) m~ be perfectly j u s t i f i e d , but that more r e a l i s t i c trapping models may be in excellent accord with the diffusion behavior. A recent discussion [5] of H-diffusion in V-Ti alloys has considered a model which takes into account several features omitted from treatments leading to eqn. ( I ) . These features may be stated b r i e f l y as follows: (I)

There is not a single unique trap site but many, according to the number of Ti atoms in the coordination she|l of Z l a t t i c e sites neighboring the i n t e r s t i t i ~ (trap) s i t e ,

(2)

Due to l a t t i c e d i l a t i o n the spectrum of trapping energies (equivalent to G in eqn. ( I ) ) depend upon specific volume and thus Ti-concentration,

(3)

Since the d i s t r i b u t i o n of H-atoms in the population of trapping sites varies with temperature, the time-averaged number of elementary jumps from a given trap type also varies with temperature. This means that Qa' the effective activation energy for diffusion, also varies with temperature.

The relations for L and Qa corresponding to the model outlined above [5] has been shown to have a particularly simple form for the V-Ti system and are written in terms of constantpressure p a r t i t i o n functions QZ(P,T) and Q~(P,T) as follows: x = [Qz(P,T)]'I ,B ~nD , Q~(P,T) Qa ~ -k ~'~[i7~-'p = Qo - Q Z - ' ~

1265 0056-9748/87 $3.00 + .00 Copyright (c) 1987 Pergamon Journals Ltd.

(2)

(3)

1264

H DIFFUSION

IN

V-Ti

Vol.

o -I

-2

-4

I0

ZO

e . x IO !

FIG. 1

Oiffuslvlty ratio X as a function of the Ti-concentratl on eu.

~ T zo e

~

3K

~

/ z

| o"

o

! IO

I 20 8.

FIG. 2

5

K~

I 30

x 102

Apparent actlvatlon energy Qa ~ of the T1-concentratlon eu.

a function

21, No.

9

Vol.

21, No.

9

H DIFFUSION

IN V-Ti

1265

where D is the d i f f u s i v i t y in the ternary system, Qo is the activation energy for diffusion in the V-H binary system, and Qz(P,T) and Q~(P,T) are given as summations over the (Z + I) d i s t i n c t trapping sites in the form,

Qz( P,T)

= Tr{~nmPneXp(-o~/kT)}

(4)

Q~(P,T) = Tr { 6nmPn~exp(-o~/kT) }

(5)

where n,m is an index labeling the number of Ti-atoms in the given i n t e r s t i t i a l site (n,m runs 0 ÷ (Z + I ) ) , Pn i~ a known density function (6) giving the density of sites of a given kind (n,m index), an~l ai is the site energy spectrum given by n o ~i = n oi + p ou

(6)

where o is the enthalpy change associated with inserting an H-atom from a reference state into a l s i t e for which n=O and the term p o takes the effect of l a t t i c e d i l a t i o n into account. In eqn. (6), p is a constant and B.~s the atomic fraction of T i . Details of the derivation of eqns. (2) + (6) are given in re~erences [5] and [ 6 ] . The tabulated results given by Peterson and Herro [1] for Qa and the pre-exponential factor 0. have been used to calculate ~ at 273 K and the results (O-symbols) plotted as functlons of the Ti-concentration in Fig. ( I ) . The data of Tanaka and Kimura [7] (Q-symbols) given in Fig. (1) were taken from these author's graphs and the k-values 0~]) of Pine and Cotts [8] at 273 were calculated from t h e i r DO and Qa values. Two features are clear from Fig. (1). I f we consider ~-data at a given temperature, then the data are in good mutual accord. The second feature relates to t~)e solid l i n e in Fig. ( I ) . This line is calculated from eqn. (2) by using the parameters ~: = -6.25 kJ/mol and p = 6.0 kJ/mol determined [5] by f i t t i n g this equation to the data of T~naka and Kimura [7] and Pine and Cotts [8] at different temperatures. •

u

The comparison between model and experiment in the case of Qa is more d i f f i c u l t since eqn, (3) predicts that Q. varies with temperature The variation of Qa with 0 is given in Fig. (2) uslng the same symbol code as Fig. ( I ) . The upper sol),d l l n e in FiUg. (2) Is Qa calculated from eqn. (3) at 273 K using the previous values of o~. and p. This l i n e agrees well with the data of Tanaka and Kimura, whose average temperature was 280 K. The lower solid line in Fig. (2) is calculated for T = 395 K and this is in reasonable accord with the Pine and Cotts data (Tave = 395 K) and those of Peterson and Herro (Tave = 351 K). •

.

~

•

,

°

•

Thus i t is apparent that the most recent d i f f u s i v i t y data [ i ] agrees well with the earlier data and with the cell model calculations outlined here. I t must, however, be born in mind that the assumption of classical jumps for H in bcc systems is clearly open to question although i t appears that the kinetic behavior in this system is at least describable in such terms• Some fundamental work in this respect has been outlined previously [5]• Acknowled~ement The author is grateful for the support provided by the Robert A. Welch Foundation. References [1] [2] [3] [4] [5] [6] [7] [8]

D. R. R. M. R. R. S. D.

T. Peterson and H. M. Herro, Met. Trans. 18A, 249 (1987). Kirchheim, Acta metall. 30, 1069 (1982). A. Oriani, Acta metall. 18, 147 (1970). Koiwa, Acta metall. 22, 1259 (1979). B. McLellan and M. Yoshihara, J. Phys. Chem. Solids. In Press. B. McLellan and M. Yoshihara, Acta metall. 35, 197 (1987). Tanaka and H. Kimura, Trans. JIM. 20, 647 (1979). J. Pine and R. M. Cotts, Phys. Rev. B28, 641 (1983).