Lattice dilation of iron by dissolved deuterium

Scrtpta

5IETALLUR{;ICA

V o l . 10, pp. 8 0 3 - 8 0 6 , 1982 Printed tn t h e U . S . A .

LATTICE DILATION OF IRON

l ' e r g a m o n t']cs-- l i d . \ 1 [ r ~ a h t q ?c
BY DISSOLVED DEUTERIUM

H. Hagi and Y. Hayashi Department of Iron and Steel Metallurgy, Faculty of Engineering, Kyushu University, Higashi-ku, Fukuoka 812, Japan

( R e c e i v e d ~Iarch 23, 1982) ( R e v i s e d A p r f l 29, 1982)

Introduction In the bcc metals which have a considerable solubility for deuterium, the Group Vb metals V, Nb, and Ta, lattice dilation due to dissolved deuterium has been studied by the measurement of the change in the volume of the metal-deuterium alloy as a function of the amount of dissolved deuterium [i]. This technique, however, is not easy to apply to iron because of the small solubility of deuterium and the plastic deformation caused by deuterium precipitation; therefore the dilational effect of deuterium dissolved in iron has not been studied quantitatively. In the present work, the elastic strain induced by a dissolved deuterium atom was measured by two independent techniques; a measurement of the change in the electrochemical permeation rate of deuterium with the application of elastic tensile stress, and a measurement of the change in specimen length as a function of deuterium concentration [2]. Experimental The specimens used were poly-crystalline membranes of electrolytic iron with average grain diameter of 17 Hm. They were annealed in vacuum at 973 K for 28.8 ks, furnace-cooled, and then chemically polished. A thin layer of palladium was electroplated on one side (anode side) of the surface of the membrane used for permeation experiments. For the detection of the lattice dilation due to deuterium absorption, a strain gauge was fixed on one side of the 0.12 mm thick membrane, and this side was covered with silicon rubber. Deuterium was charged at a constant cathodic current density ic. The cathodic electrolyte was a 0.5 k~nol/m3 D2SO ~ + D20 solution, and the anodic electrolyte was a 0.2 kmol/m ~ NaOH + HoO solution. Results and Discussion When the deuterium permeation maintained a steady state permeation current, an elastic tensile stress was applied to a specimen. As shown in FIG.l, a new transient appeared, and after the permeation current attained a new steady state, the stress was released. The permeation rate decreased to the value which it had before the application of stress. Thls procedure was repeated with an increase in the applied stress. Figure 2 shows a plot of the logarithm of the ratio of the permeation rate in the stressed condition to that in the unstressed condition, log(Jo/J0), against applied stress o. The increase in the deuterium permeation rate with the stress application can be attributed to the following causes; (i) change of kinetic parameters of the deuterium evolution reactions at the cathodic surface, (ii) increase of the diffusion coefficient of deuterium, and (iii) increase of the deuterium solubility (decrease of the chemical potential of dissolved d e u t e r i u m ) If the kinetic parameters of deuterium evolution reactions change with the stress application and the amount of deuterium atoms adsorbed on the surface increases, the deuterium permeation rate increases. Despic et al. [3] reported that the application of an elastic tensile stress shifted the corrosion potential of Armco iron to a nobler potential. Also relevant to the kinetics, we examined the effect of stress on the permeation of deuterium through the specimen by polarizing potentiostatically. The value of log(Jo/J0)/o in the potentiostatic condition (ic = i0 A/m 2) proved to be equal to that in the galvanostatic condition (ic = i0 A/m2).

803 0036-9748/82/070803 045O5.0O/O C o p y r i g h t (c) 1982 P e r g a m o n P r e > s l t d .

804

DILATION

OF

IRON

BY

DEUTERIUM

Vol.

16,

No.

7

This suggests that the change in the deuterium evolution rate with the stress application is negligible at the current density around i0 A/m 2. The permeation rate J(t) of deuterium was measured in the unstressed and stressed conditions. Figure 3 shows the time required for attaining the steady state permeation rate, J(~). Because the curves are superimposable, the diffusion coefficient of deuterium is concluded to be independent of the application of stress [4]. If the increase in the deuterium permeation rate with the application of stress is attributed to the decrease in the chemical potential of dissolved deuterium, the strain of the iron lattice induced by deuterium dissolution, which interacts with the applied stress, can be obtained. The strain of a unit cell of the iron lattice containing one deuterium atom can be calculated from the following equation on the assumption that the strain field around a deuterium atom is purely dilatational [i]: In(Jo/J0)/o

=

a3~/kT,

(i)

where a is the lattice parameter, ~ an average of the diagonal elements of the strain tensor due to the introduction of a deuterium atom into a unit cell of iron, k the Boltzmann constant, and T the absolute temperature [2]. The value of ~ for deuterium in iron calculated from the data (FIG.2) is 0.057 at 296 K, and this value is equal to that obtained for hydrogen in the same procedure [2] and nearly equal to that calculated from the hydrogen partial molar volume obtained by Bockris et el. (g = 0.065 at 300 K) [5]. The dilation of iron by cathodic deuterium charging was directly measured by using a strain gauge and a dynamic strain amplifier. Figure 4 shows laboratory records of the effect of deuterium charging on the output of the dynamic strain amplifier. The output changes with time even in the uncharged condition, and the output in the charging condition is large as compared with the value obtained by extrapolation of the output in the uncharged condition. The dilation of the specimen was calculated from the increment of the output due to cathodic polarization. The specimen length changes reversibly with switching on and off the cathodic current below ic = I0 A/m 2. At higher current densities, however, the specimen length did not recover to the length of an uncharged specimen because of the occurrence of the plastic deformation due to blister formation [2]. The lattice dilation eD(t = 30 sec) at 30 sec of charging time is shown in FIG.5. We measured the change in the specimen length due to cathodic polarization using 50 % coldworked specimens to determine the experimental condition under which the thermal expansion becomes negligible. The diffusion coefficient of deuterium in iron (D) depends on dislocation density, and at room temperature D in a 50 % cold-worked specimen is much smaller than D in an annealed specimen [6]. Therefore, in a cold-worked specimen no lattice dilation due to dissolved deuterium is expected to occur in a short charging time. On the other hand, because the coefficient of thermal expansion in a cold-worked specimen is the same as that in an annealed specimen, it can be confirmed by comparing the length changes in these specimens that the thermal expansion is negligible under the condition of the present experiment: The lattice expansion was not observed within 30 sec of charging time in the 50 % cold-worked specimen polarized cathodically with i c ~ i0 A/m 2. In an annealed specimen, however, the lattice expansion due to dissolved deuterium is observed under these charging conditions as shown in FIGs.4,5. Deuterium was introduced from one surface (the cathodic surface) of a membrane and the lattice dilation at the opposite surface was measured by using a strain gauge. In order to know the relative lattice dilation per atomic fraction of deuterium dissolution, the concentration of dissolved deuterium at the opposite surface Co(t) needs to be determined. However, the value of Co(t) can not be directly measured. Therefore, we calculated Co(t) from the concentration of dissolved deuterium at the cathodic surface C k and the diffusion coefficient D of deuterium. Permeation transients of deuterium were measured in annealed specimens and the diffusion coefficient D of deuterium was determined to be 4 x 10 -9 m2/s at 296 K [4]. The content of dissolved deuterium is not zero in the specimen prior to the commencement of cathodic polarization because of the corrosion of the cathodic surface. The deuterium permeation rate before cathodic polarization J(O) and the permeation rate at 30 sec of charging time J(30 s) were measured by the electrochemical permeation method. J(30 s) is approximately a steady state permeation rate. The increment in the deuterium concentration AC k at the cathodic surface by the polarization can be calculated from the values of J(0) and J(30 s):

~ol.

10,

No.

v

D I L A T I O N OF

IRON BY DIIUI'ERIU~I

J(30 s) - J(0) where L is the specimen thickness.

~

8,/5

D%Ck/L,

(2)

The variation of £C k with ic is shown in FIC.6.

An exfoliation of the silicon rubber on the measuring surface was not observed during deuterium charging. This suggests that the rate of deuterium degassing at the measuring surface is very small and deuterium is distributed nearly uniformly in the specimen after a sufficiently long time of charging. Assuming that the strain field around a deuterium atom is purely dilatational and an interstitial site occupancy is ramdom, the macroscopic change of specimen length ;D(t) can be ~iven by

ED(t )

2sACo(t) "

where £C o is the increment in the deuterium concentration at the measuring polarization.

(3) surface by cathodlc

As described above, because deuterium is distributed nearly uniformly in the specimen polarized for a long time, say 30 sec, ACo(30 s) is nearly equal to AC k. Substitution of the value of ~ obtained in the permeation experiment to eq.(3) gives SD(30 s)

-

0.I14~C k.

(4)

The value of SD(30 s) calculated from eq.(4) is shown by the dashed curve in FIG.5. The experimental value of eD(30 s) shows scatter, but the experimental and calculated values of SD(30 s) are considered to be equal within experimental error, i.e., the same value of ~ can be obtained from the dilation and permeation experiments. Conclusion The elastic dilation of electrolytic iron by dissolved deuterium was measured by two independent techniques; a measurement of the change in the electrochemical permeation rate of deuterium with the application of elastic tensile stress, and a measurement of the change in specimen length as a function of deuterium concentration. The deuterium permeation rate increases with the application of stress but the diffusion coefficient of deuterium does not change, so that the stress application affects the solubility of deuterium in iron. The logarithm of the ratio of the permeation rate in the stressed condition to that in the unstressed condition (in(Jo/J0)) is proportional to the applied stress (o). The strain of a unit cell of the iron lattice containing one deuterium atom can be calculated from the fractional increase of the permeation rate with increasing stress (in(Jo/J(1) /o). The value of e, the average of the diagonal elements of the strain tensor, is 0.057 for deuterium (at 296 K). This value is the same as that for hydrogen. The dilation of the iron specimen by cathodic deuterium charging was measured by using a strain gauge and a dynamic strain amplifier, and the concentration of dissolved deuterium was measured by the electrochemical permeation method. The change in specimen length with cathodic deuterium charging is reversible and the thermal expansion of the specimen is negligible at a small cathodic current density. The value of a obtained from the relative dilation of the specimen per atomic fraction of deuterium dissolution is the same within experimental error as that obtained from the permeation experiment. References [i] [2] [3] [4] [5] [6]

H. Peisl: Hydrosen in Metals I, Ed. by G. Alefeld and J. V~ikl, Springer-Verlag, New York, (1978), p.53. H. Hagi, Y. Hayashi and N. Ohtani: J. Japan Inst. Metals, 46, 141 (1982). A. R. Despic, R. G. Racheff and J. O'M. Bockris: J. Chem. Phys., 49, 926 (1969). H. Hagi, Y. Hayashi and N. Ohtani: J. Japan Inst. Metals, 42, 801 (1978); Trans. JIM, 20, 349 (1979). J. O'M. Bockris, W. Beck, M. A. Genshaw, P. K. Subramanyan and F. S. Williams: Acta Met., 19, 1209 (1971). M. Nagano, Y. Hayashi, N. Ohtani, M. [sshiki and K. Igaki: J. Japan Inst. Metals, 45, 178 (1981); Trans. JIM, 22, 423 (1981).

806

D I L A T I O N OF IRON BY D E U T E R I U M

Vol.

16, No.

7

/

,,/o 0010 i

0 ~0

/" g':69MPa OMPa 69MPa OMPO 78MPs OMPa

~r

78MPO 0W~

o~ooos

~00~

o/° T = 296 K

,

i

0

I00

i

200 /

T~me

,

A

300

400

4

s

O"

FIG.I A laboratory record of the effect of elastic tensile stress on the steady state deuterium permeation current.

,.:_

6)/~/ /6 ) /

6) 6)

L

6)

/

/,

i

5

0

78

485 m m T = 288 K

/

0

0

o

10 Time

I

=

i¢off

i~~,on _ I

6

~

,~ = 10 A i m ~

/

=

•

c

~h0 ~J"

ic I A m 2

/ I

,o

I

7

E

0"I MPa

oOS

;0

MPa

FIG.2 Logarithm of the ratio of the deuterium permeation rate in the stressed condition to that in the unstressed condition as a function of stress.

10

e

;0 /

0

i

i

I5

20

"5 "5

I

8

L3o,

25

--

FIG.4 Laboratory records of the effect of cathodic deuterium charging on the output of a dynamic strain amplifier.

. . . .

u

i

0.10

T =296 K

3

Time

S

FIG.3 Time required for attaining the steady state permeation of deuterium is not affected by the application of stress.

I

o f ./

E

d

!

oJ.

0.05

./ T = 296 K

e/ .,~ O / n

0

2

4 i:

I

6 A m -2

8

tO

FIG.5 Variation of the elastic dilation due to dissolved deuterium ED(30 s) with ic. Dashed curve is calculated from eq.(4).

0

i

2

!

4 ~c

I

6 A m -z

i

i

8

10

FIG.6 Variation of the increase in the dissolved deuterium concentration AC k at the cathodic surface by polarization with ic.