Solid solutions of hydrogen in gold, silver and copper

J. Phys. Chem.Solids, 1973,Vol.34, pp. I 137-1141. PergamonPress. Printedin Great Britain

SOLID S O L U T I O N S OF H Y D R O G E N IN G O L D , SILVER AND COPPER R. B. McLELLAN Department of Mechanical and Aerospace Engineering and Materials Science, William Marsh Rice University, Houston, Texas 77001, U.S.A. (Received 31 May 1972)

Abstract--The temperature variation of the hydrogen solubility of copper, silver, and gold in equilibrium with H2-gas at atmospheric pressure has been measured. Values for the relative partial enthalpy and partial excess entropy of the interstitially dissolved hydrogen atoms have been estimated from the solubility data. The experimental data are compared with those of previous investigations. The partial entropy values obtained for copper and silver show a 'regular' behavior when compared with partial entropies for other cubic metals having a small occludive capacity for hydrogen. The gold-hydrogen system is, however, anomalous and has a partial excess entropy which is essentially zero.

1. INTRODUCTION

THIS work is part of a program of hydrogen solubility determinations designed to fill some of the existing gaps in the knowledge of the thermodynamic functions of hydrogen in metals. The noble metal triad copper, silver, and gold forms an interesting series. In the case of gold there is only one previous determination of the hydrogen solubility[i]. The values of the relative partial enthalpy A/~n and excess entropy AShxs of dissolved hydrogen obtained from the Arrhenius plot of these solubility data do not fit into the correlation pointed out by Gallagher and Oates [2] in which there is a linear relation between A/1H and ASH ~s for f.c.c, and C.P. Hex. metals. In the case of the silver-hydrogen system the solubilities determined by Steacie and Johnson [3] and Siegelin, Lieser and Witte [4] are in good accord. However, the later solubilities determined by Thomas[l] are about two orders of magnitude smaller than the previous determinations. The copper-hydrogen system on the other hand has been extensively investigated. However, there is considerable variance between the results obtained in several investigations. The results of Thomas

[1], Eichenauer and Pebler[5], Lieser and Witte [6] and Rtintgen and Mtiller[7] are all in good mutual accord, whereas the data of Sieverts and Krumbhaar[8] and Himmler[9] show considerably higher hydrogen solubilities. 2. EXPERIMENTAL PROCEDURE

The hydrogen solubilities were measured by equilibrating the cylindrical solvent metal samples in super pure hydrogen gas, quenching the hydrogenated samples, and determining the amount of hydrogen occluded by a hot extraction technique. The experimental procedure has been described in detail previously [10,11]. Because of the low solubility of hydrogen in the metals investigated, massive samples were used in order to insure that the amounts of hydrogen occluded, even in equilibrations performed at the lower temperatures employed, were within the range where they could be measured accurately in the hot extraction procedure. The cylindrical samples weighed 24.94g (Cu), 73-55 g (Ag), and 142.88 g (Au). The material used was MARZ-grade metal supplied by Materials Research Corporation. The super pure hydrogen had a nominal purity

1137

1138

R.B.

McLELLAN

of 99.9995 per cent by volume and less than 1 ppm by volume of hydrocarbons). Due to the large mass of the metal samples, the Pt-13% Rh thermocouples could not be used for supporting the samples as in the previous experiments [10, 11]. In the present investigation half-round grooves were machined along the length of the cylindrical samples, leaving a small length of metal intact at the center (see Fig. 1). Small holes were drilled through this bridge of intact metal and P t - R h support wires were threaded through the holes. ~uppor ires

t __.___-.--~ ~

Table 1 T~

Copper 0 • l0 s

1027 1005 939 911 871 846 809 778 755 723 659 609 594

T~

7"20 7'17 4.88 4.21 3"55 3"10 2"33 2"33 1"90 1"54 0"931 0"698 0"552

Gold 0 • 106

1050 997 948 939 910 878 838 805 793 777 735 693

T~

2.86 2-51 2-23 1-93 1"96 1"96 1"66 1'66 1-66 1'30 1'27 1.06

941 921 881 857 834 810 750 727 703

Silver 0 • 106 6"17 5.94 4.24 3.90 3-15 3'21 2'25 1'83 1'51

10-4

o This Invostlgotloa

hermocouple Wires

~J

<~LimSer ~ Wttfe (~R~ntgoa ond M~ller

-%

I I I I 10-5

I I I I I I

Fig. 1. Sample geometry.

In a series of preliminary experiments several pairs of thermocouple wires were spot welded onto the sample at various positions along its length. Experiments at both high and low temperatures showed that detectable temperature gradients were not produced and the sample was heated uniformly by the high frequency coil. Since no diffusivity data are available, from which equilibration times could be estimated, a series of low temperature equilibrations was performed for varying times. By this means it was ensured that the equilibrations were performed for times long enough to achieve saturation. 3. RESULTS

The experimental data are shown in Table 1 and in graphical form in Figs. 2 (Cfi) and

,o 7.0 ;.5

~.o

,'.,

~.o

~.~

,&o xlO

,&5 0K'l

~;.o

,;.5

,~,.o &., ,3.o

9

Fig. 2. V a r i a t i o n o f the H - s o l u b i l i t y in solid copper with temperature.

Fig. 3 (Au and Ag). The solubility unit employed is 0, the atom ratio of hydrogen (NH/N,v). It is assumed that in the f.c.c. solvent metals the hydrogen occupies the octahedral interstitial sites[12] so that 0 is also equal to the fraction of available sites occupied by the solute atoms. In the case of copper (Fig. 2), the present data are in good general accord with the previous investigations[l, 5-7], except for the high values of Sieverts and Krumbhaar [8] and Himmler [9]. For silver (Fig. 3), the present data are in

SOLID SOLUTIONS OF HYDROGEN IN GOLD, SILVER AND COPPER I0-'

r

I

I

I Hydrogen

I in S i l v e r

I -a n d Gold

id 5

t

8

i0-~ Silver ~' Data of Thomas . . . . o This Investigation--

"", "'~. "

Go d ~ Data of Thomos-cl This InvesticJCltion~

Steacie and dohnson $iegelin,l-leser and Witte

IO 7 . 0

I

I

8.0

9.0

I

I

I

I

I0.0

II.O

12.0

13.0

~- x 10't *K-t~

Fig. 3. Variation in the H-solubility in solid silver and gold with temperature. agreement with the magnitude found by T h o m a s [ I ], although the slope of the Arrhenius plot is somewhat different. T h e much larger solubilities found in the sets of investigations shown in Figs. 2 and 3 is not understood. A tentative suggestion is that it could be due to using a Sieverts apparatus made from quartz, which is known to absorb considerable quantities of hydrogen at high temperatures. In this context it should be noted that in the H-analyses of the present experiments, the outgassing was performed under vacuum in a quartz tube. H o w e v e r , the walls of the tube were held at room temperature by cold air blast. The present data for gold are somewhat lower than these given by T h o m a s [ 1].

1139

valid for quasi-regular interstitial solutions [ 13]. T h e values of A/~n and ASHx~found from a least-squares regression to the data points are given in Table 2 and a Fig. 4 shows plots of In 0 vs l I T . T h e values of ASnx~ can be read from the ordinate of Fig. 4. T h e values of A/qH found for hydrogen in copper, silver and gold are in qualitative agreement with the well-known periodic variation of this quantity with the position of the occluding_ metal in the Periodic Table [11]. Plots of AHn vs G r o u p N u m b e r show that there is a high maximum in all three Long Periods at G r o u p II followed by a steep drop to a minimum at G r o u p VI followed by a more gentle rise to another but lower maximum at G r o u p V I I I C , followed by a rapid decrease in AHH The values of A/~H obtained for the 1B metals in this investigation are in good accord with this trend. Furthermore, a perusal o f the A / ~ . - - A~. x~ correlation proposed by Gallagher and Dates [2] shows that the data obtained here for the C u - H and A g - H systems are in reasonable Table 2

Solvent Cu Ag Au

All,

AS ~ s

k.cal/g.at.H

e.u.

13.11 _+0.34 13.56• 6.58 _+0.36

-8.87___0-61 --12.69--+0.92 -20.46-+0.83

4. DISCUSSION The relative partial molar enthalpy AHH and relative partial molar excess entropy A S h x~ with respect to H2-gas at one atmosphere pressure can be obtained from the experimental results using the equation, In0=

A/Ill RT

4

AS. ~ R

(1)

,11

.IZ -13 -14

Gold

--,,

;

~

~

,

~

~

,

;

,"

,',

12

10 r . K - I

T

Fig. 4. Plot of In 0 vs I/T for solutions of hydrogen in solid copper, silver and gold.

1140

R.B.

McLELLAN

accord with the correlation. H o w e v e r the data for the A u - H system are at variance with this correlation. According to the correlation [2], a metal for which A/~n is 6.58 k.cal/mole, should have ASh ~ ~ -- 11-5 e.u. The value found in this work is -- 20.46 e.u. and that estimated from the solubilities o f T h o m a s is - 17.6 e.u. It may be more enlightening to compare the values of ,~n~ instead o f A~,~. Accordingly Sn ~s has been obtained for a series o f f.c.c. and C.P. H e x solvent metals from the corresponding AS, ~s values using thermodynamic data for gaseous hydrogen [14]. T h e value of S ~ used referred to the mean experimental temperature. T h e data for the R h - H , R u - H , and I r - H systems were taken from the work o f Oates and McLellan [ 11 ] and those for a-Ti, and Co from the compilation of Gallagher and Oates[2]. T h e values of Sn ~ are given in Table 3. It can be seen that, with the exception of Au, the Sn~S-values show only small variation from metal to metal. This relative constancy in SNx~ has been pointed out previously [15] and is useful since, in dilute solutions, A/~n can be taken as a direct measure o f solubility. H o w ever, the value for Sn ~ for H in gold is virtually zero. T h e Su~-data presented in Table 3 refer to very dilute solutions. Thus it is safe to assume that Sn ~ does not contain any terms due to deviations from the ideal configurational entropy. E v e n for much more concentrated Table 3 Solvent metal Au Ag Cu Rh Ru a-Ti Co Ir

-

ASh xs

e.u. 20.46 12.69 8.87 I 1-99 10-84 13"09 10"27 10.21

T-Range ~

Sit xs k

693-1050 703-941 594-1027 858-1542 1002-1503 480-950 600-1200 1393-1581

- 0.06 3.75 5.63 4.65 5.29 3"33 5"06 5.54

interstitial solid solutions, where deviations from Henrian behavior occur, the deviations have recently been ascribed to non-ideal enthalpies rather than non-random entropies. See, for example recent work on 7 F e - c solutions [ 16] and N b - H solutions [ 17]. If it is assumed that H dissolves as a screened proton in metals[18], it may not be too unrealistic to assume that the contribution to Sn xs due to the proton itself is independent of the solvent metal and that the strength of the elastic distortion it produces is also independent of the solvent metal. If this were the case ~ x s would be proportional to the strain produced by a dissolved H-atom. In fact [19], ~nxs oc fllxSrv3 + a constant.

(2)

where /3 is the thermal expansivity, /z the shear modulus, ~ the displacement caused by the H-atom and defined in the form [20], 8 = rt~ -- ( V ~ - - l)r,~ W~rv

(3)

where rv is the radius o f the solvent atoms and rn that of a proton. Taking the Goldschmidt radii for rv and assuming rn = 0.65.~, the quantity/3/zSr~ 3 has been calculated for the metals in Table 3. T h e constants used and results obtained are shown in Table 4. F o r the metals Au, Ag and Cu the elastic data (C44) of Simmons [21] were used: for R u , / ~ was estimated from the Youngs' modulus given by Simmons and Wang [22]; for It, the C44-value of Simmons and Wang[22] was used and finally tx for Co and o~-Ti was taken from extrapolations of the Youngs' modulus measurements of K6ster [23]. It should be noted that the quantity fltz~r~ 3 is proportional to the entropy arising from the dilation of the solvent lattice. T h e r e is an entropy term arising from the shear strain but this is proportional to ~z and is assumed to be negligible. T h e quantity /3~Srv ~ is plotted against Snx~/k in Fig. 5. It can be seen that the correlation is quite reasonable but unfortunately

SOLID S O L U T I O N S OF H Y D R O G E N

IN G O L D , SILVER A N D C O P P E R

1141

Table 4 Solvent metal

Au

fl • 105 p~x 10-1~ dyne/cm ~ b • 10e r~,3~lx8• 10TM dyne.cm S,~S/k

I

I

l

l

l

l

l

i

i

J

l

l

~

Ag

Cu

Rh

Ru

a-Ti

Co

Ir

1-70 0.753

0.84 1-41

0.82 1.78

0.82 0.385

1-24 0.747

0.65 2-60

1,39 0.420

1.89 0.430

2.70 4.63

2.60 6.37

6.60 17.8

5-00 14"2

5.10 18.07

2.10 2-05

7.50 13"6

4-66 19.45

-0.06

3.75

5.63

4,65

5.29

3-33

5.06

5.54

l

l

l

l

i

l

l

l

I 15

~

~9 ct-T i

k

I 0

,

t

i 5

i

L

rv3)~lu.a

I I0

l

i

x I019

i

i

i

t 20

dyne. cm ~

Fig. 5. Correlation between S, =s for various metallic solvents and r,,3/3/x8.

(see Table 4) it does not provide an explanation of the anomalously low value of ~ s found for the Au-H system. It should be mentioned that the correlation in Fig. 5 does not purport to be a "serious" theoretical model for Sn xs since, in addition to being based on the assumption that 6 is constant for all the metals (supposedly elastically isotropic), other contributions to SH~s, such as those arising from electronic changes [24], have been neglected. There is, however, no constant volume to constant pressure correction[25] involved in comparing S,~S (measured) with/3/~arv3. A c k n o w l e d g e m e n t s - T h e author is grateful for the support provided by the Robert A. Welch Foundation and the National Aeronautics and Space Administration.

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A 1 M E 245, 179 (1969). 3. S T E A C I E E. W. R. and J O H N S O N F. M. G., Proc. R. Soc. Ser. A. 117, 662 (1928). 4. S I E G E L I N W., L I E S E R K. H. and W I T T E H., Z. Elektrochem. 61, 359 (1957). 5. E I C H E N A U E R W. and PEBLER A., Z. Metallkunde. 48, 373 (1957). 6. LIESER K. H. and W l T T E H., Z. Phys. Chem. 202, 321 (1954). 7. R O N T G E N P. and M O L L E R F., Metallwirtschaft 13,81 (1934). 8. S I E V E R T S A. and K R U M B H A A R P., Z. Phys. Chem. 77, 591 (1911). 9. H I M M L E R W., Z. Phys. Chem. 195, 224 (1950). 10. OATES W. A. and M c L E L L A N R, B., Scripta Metall. 6, 349 (1972). 11. M c L E L L A N R. B. and O A T E S W. A., Acta Metall., to be published. 12. W O L L A N E. O., C A B L E J. W. and K O E H L E R W. C.,J. Phys. Chem. Solids 24, 1141 (1963). 13. M c L E L L A N R. B., Mater. Sci. Engng 9, 121 (1972). 14. W O O L E Y H. W., SCOTT R. B. and BRICKW E D D E F. G.,J. Res. Nal. Bur. Std. 41, 379 (1948). 15. M c L E L L A N R. B., In Phase Stability in Metals andAlloys (Edited by P. S. Rudman, J. Stringer and R. I. Jaffe), McGraw-Hill, New York (1967). 16. M c L E L L A N R. B. and D U N N W. W., Scripta Metall. 4, 321 (1970). 17. O ' K E E F F E M. and S T E W A R D S. A., Proceedings o f the Conference Hydrogen in Metals, Kernforschungsanlage, Jiilich, Germany, Vol. 1, p. 23 (1972). 18. E B I S U Z A K I Y. and O ' K E E F F E M., Prog. Solid St. Chem. 4, 187 (1967). 19. M c L E L L A N R. B. and SHUTI~LEWORTH R., J. Phys. Chem. Solids 24, 453 (1963). 20. M c L E L L A N R. B., Trans. A I M E 230, 1468 (1964). 21. S I M M O N S G., Journal o f the Graduate Research Center, Vol. 34, Southern Methodist University, Dallas, Texas (1965). 22. S I M M O N S G. and W A N G H., Single Crystal Elastic Constants and Calculated Aggregate Properties. Second Edition, M.1.T. Press, Cambridge, Massachusetts (I971). 23. KOSTER W.,Arch. Eisenhiit. 14, 271 (1940). 24. OATES W. A. and F L A N A G A N T. B., SolidState Commun. 9, 1841 (1971). 25. W A G N E R C.,Acta Met. 19, 843 (1971).