the diffusion of hydrogen through palladium

The Diffusion of Hydrogen through PalladiumAuthor(s): Alfred HoltSource: Proceedings of the Royal Society of London. Series A, Containing Papers of aMathematical and Physical Character, Vol. 91, No. 626 (Feb. 1, 1915), pp. 148-155Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/93596 .

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148

The Diffusion of Hydrogen through Palladium.

By ALFRED HOLT, M.A., D.Sc.

(Communicated by G. T. Beilby, F.R.S. Received June 25, 1914.)

(From the Muspratt Laboratory of Physical and Electro-Chemistry, University of Liverpool.)

The diffusion of gases through metallic septa has been the subject of much

investigation, for by examining the change in the rate at which the gas diffuses with varying pressures the physical condition of the intrametallic

gas has been deduced. In this field of research hydrogen-palladium has probably received the

closest attention, and as the same conclusions have not always resulted from the experimental evidence, little excuse is necessary in presenting new data. Schmidt,* who determined the rate of diffusion between 150? C. and 300? C., and for various pressures, concluded that while the temperature curve is probably quadratic, the pressure curve for the higher pressures may be linear,. results which have been questioned by Richardson,t since the experimental data when applied to this latter author's formula for rates of diffusion gave indecisive results.

Winkelmann} had previously expressed the view that the dissociation of the hydrogen molecules was necessary to explain the observed phenomena of diffusion, a contention considered unnecessary by Schmidt, though by assuming it Richardson calculated the heat of dissociation of one gramme- molecule of hydrogen from Schmidt's experimental results, and Winkelmann has since? reaffirmed his original conclusion.

Previous to these authors Ramsayll had made the interesting observation that hydrogen diffusing through palladium into an atmosphere of an indifferent

gas never diffused till its partial pressure on the two sides was equal. The,

pressure was, finally, always greater on the side from which the gas entered the metal.

Recently the present writer, in conjunction with Edgar and Firth,? has shown that, while the rate of diffusion becomes more rapid with rise of

temperature, any particular temperature is not characterised by any definite rate of diffusion. The rate depends on what we have called the " activity '~

* 'Ann. Physik' (iv), vol. 13, p. 747. + 'Camb. Phil. Soc. Proc.,' vol. 13, p. 27 (1905). + ' Ann. Physik,' vol. 6, p. 104 (1901). ? 'Ann. Physik,' vol. 16, p. 773 (1905). |I 'Phil. Mag.,' vol. 38, p. 206 (1894).

? ' Zeit. Phys. Chem.,' vol. 82, p. 513 (1913).



The Dijfftsion of Hydrogen through Palladium.

of the metal, i.e. its power of rapid occlusion of gas, and the greater the

activity the greater the rate of diffusion. The apparatus and method employed in the following experiments need not be figured or described in detail, since it was essentially the same as that already illustrated,* but a few general remarks may not be out of place.

The experiments group themselves under three heads as follows, and except in two cases represented a temperature range of 130? C. to 300? C.

(1) Measurement of the rate of diffusion from a constant pressure into a

vacuum, (2) measurement of the rate of diminution of pressure into a maintained vacuum, and (3) measurement of the rate of diminution of pressure on one side, and increase of pressure on the other side, of a palladium septurn during the diffusion of a definite volume of hydrogen.

The actual volume of gas diffusing through the heated metal was not determined, only the variation of pressure with time being recorded, the rate

being taken to be the number of seconds required for a change in pressure of 1 mm. At the temperatures of the experiments palladium becomes saturated with hydrogen very rapidly, and hence it was only necessary to wait a few minutes after the commencement of each experiment before readings could be begun. It was found that in every experiment a graph in which the

logarithms of decreasing pressures were plotted against time yielded with considerable exactness two straight lines cutting one another at some definite

point. In the case of increasing pressures the graph of the logarithms of atmospheric pressure (760 mm.) minus the observed increasing pressure gave two straight lines when plotted against time.

These graphs for a series of experiments are illustrated in the figure; they represent the experimental data given in the Tables later in this paper.

The relation may therefore be expressed:-

1 log1 =I K for decreasing pressure, t p2

and I log 760 -- = K for increasing pressure. t 760-p2

From these relations it is apparent that the gas is diffusing through the metal at a rate proportional to the pressure, not to the square root of the

pressure, and hence according to the partition law the intramolecular gas is in a simple molecular condition.

It is, however, doubtful whether such a conclusion as to the molecular state of the gas is justified, for the occlusion of hydrogen by palladium is a far from

simple phenomenon.

* 'Zeit. Phys. Chem.,' vol. 82, p. 533 (1913). 2

149



150 Dr. A. Holt.

It?has already been mentioned that the value of K calculated from either of the above expressions does not usually remain a constant throughout the whole range of pressures examined (100 to 700 mm.), but has two different

0 Time -

values, one for the initial and the other for the final portion of the rate curve.

Reference to the graphs above will show, however, that though the rate

curve can be closely represented by two equations of either of the above types




giving different values of K and exhibiting a definite point of transition from one value to the other, this can only be an approximation, for the phenomenon of diffusion is perfectly continuous. Further, it does not hold for pressures lower than about 90 mm., where the rate begins to diminish rapidly, and does not appear to be proportional to any definite function of the pressure.

In a recently published paper,* the author has shown that the rate of solution of hydrogen at constant pressure by palladium foil cannot be

represented by a simple expression since there is a discontinuity, in the rate curve, which consists of two portions of the same general curvature. The peculiar form of these rate curves has been attributed to two modifica- tions of the metal, differing solely in the packing of the particles. The

discontinuity of the value of K in the present experiments on diffusion almost certainly arises from a similar cause, for as the temperature increases the discontinuity becomes less, just as has been observed in the case of the rate of solution. It is unfortunately impossible to measure the rate of diffusion through palladium black to see whether the discontinuity of K ceases, but the close parallelism between the phenomena of solution and diffusion in palladium foil, and the explicability of the former, on the basis of metallic allotropes, points to a similar explanation in the case of the results given in the present communication.

It might be argued from an inspection of the graphs and data given in the

following Tables that neither value of K in any given experiment is really a

constant, but is continually and slowly altering. This is probably true, and as has been mentioned it is only an approximation to represent the graphs by straight lines, but the variation from the rel'tion

Rate x pressure = constant

is so slight as to be easily explained by the changes of solubility of gas in the metal with pressure.

If at any given temperature we suppose the amount of gas retained by the metal to be the same as that occluded at a pressure equal to the mean value of the pressures on either side of the metallic septum, then as diffusion

proceeds this mean pressure will vary, and so will the gas-content of the metal. Since the rate of diffusion has been shown to vary from one experiment to another at the same temperature and to depend on the activity of the metal, it follows that the amount of gas retained and the speed with which it

adjusts itself to the ever varying pressure must have some slight influence on the rate of diffusion.

At temperatures over about 1200 C., the change in the solubility of

* BRoy. Soc. Proc.,' A, vol. 90, p. 226 (1914).

151



Dr. A. Holt.

hydrogen in palladium between 380 min. and 710 mm., or 380 mrr. and 50 mm. (the mean values of the pressures on the two sides at the beginning and end of an experiment) is not great, and hence there is no pronounced variation between the experimentally determined points and the' straight lines of the graph.

The following Tables contain data of a few of the many experiments carried out. The pressure readings in brackets ( ) were not determined experimentally, but were read off the graphs as the intersection point of the two

straight lines. Series I gives examples of the rates of diffusion into a vacuum from constantly maintatained atmospheric pressure. Series II represents the rate of diminution of pressure into a maintained vacuum, while Series III shows the rate of diminution of pressures on one side and the corresponding rise of pressure on the other.

The figures in heavy type show the pressures at which the second value of K begins. They represent the intersection of the straight lines on the graph, or, what is the same thing, the pressure at which the values of

logl = K t2--t p2

show marked variation.

Conclusion.

Between 700 mm. and 100 mm. pressure hydrogen appears to diffuse

through palladium heated to about 100? C. to 300? C. at a rate proportional to the pressure of the gas, though the rate curve appears to consist of two

portions. It is shown that by assuming the pressure-time curve to consist of two exponentials of different slope, the experimental values can be reproduced with considerable accuracy, certainly with an accuracy which leaves no

question as to the proportionality of the rate to the pressure, not to the

square root or any other power of the pressure. As in the case of the rate of solution of hydrogen at constant pressure by

palladium foil where discontinuous curves are obtained, the two exponentials of different slope are accounted for by metallic allotropes.

At pressures lower than 100 mm. the rate of diffusion becomes more and more slow, and is not apparently related to any simple function of the

pressure.

152



Series I.

Temperature, 140? C. Temperature, 200? C. .Temperature, 260? C.

Time.

Calcu- lated

Observed. from mean

| value of I K.

K

lot 760-p2)

Time.

Calou- I lated

Observed. from mean

| value of iK.

Pressure observed.

mm. 25

90

150

204

272

348

380

407

457

502

544

588

618

649

665

K

( -- 760-p

n .Anrft i u V<v j

0 020

0-020

0 -020

0-019

0 -019

0 -016

0 017

0 -016

0-016

0 015

0-015

0 -015J

0 * 11

I C'

O l rl 0

a a :

Time.

Calcu- lated

Observed. from 1mean value of

K.

min. imiln. 0 0-0

5 4-4

10 10 -2

15 15'-6

20 1 21-2

25 26 0

30 - 30-9

35 36-3

40 41 -2

45 45 9

50 50 -7

55 55 3

65 64 -9

75 73 .4

85 82 3

Pressure observed.

mm. 17

118

230

317

393

447

495

539

573

601

625

645

678

700

717

K I

log )0.:2 I/

0 013'

0'014

0 -015 0-015

0015

0-015

0 014

0-015

0-015

0 014

0-014

0'014

0 014

0 -014J

-p

0

a

c,

3

<?.

0 fw

o

t;sr

r

.0

c

C'

,<

C, .

ZiS

c3>

?-i

Cs

Pressure observed.

mm.

127

192

252

303

349

391

433

458

487

513

534

550

570

585

630

m1in. 0

10

20

30

40

50

61

70

81

91

101

111

121

131

170

min. 0-0

10 0

20 3

30 0

39 '8

49 8

60 *9

69 8

810 '

92 1

102 6

110'2

121 '4

130 6

163 4

t-

C3 CO

If

0 0047'

0 -0048

0 '0047

0 -0047

0-0047

0 -00479

0 0038

0 0039

0 0041

0 0040

0-0038

0 0039

0 0039

0 0037J

niun. 0

2

4

6

9

13

15

17

21

25

30

37

43

50

55

min. 0 0

2 0

4'1

6 -1

9 0

12-7

14 5

16 6

20 -7

25 1

30 0

36 3

41 5

48 3

52 '6

. .... ..... . .............................................. . . .

I~~~~ ~ ~"":~' _" .2.`

I , I

I

i I I i i

II

I

I

I

i

i

I

i I

i

I

I

i

i

i

I

i

i

i

I

I 1

i

i

Ii

I

i

I I

I

f

i i

i

I i

i

i

i

i

I

I

i

. i

I

11

li

I

i

i

i

I

I I



154 Dr. A. Holt.

Series II.

Time. Timle. -- Pressure Pressure K

Calculated observed. (log Calculated observed. ( log Observed. from mean t p2/ Observed from mean P2

value of K. value of K. . _ _ _ _ _~~~~~~~~~~~~~;

Temperature, 70? C. min.

0'0

3 9

10 1

15 0

23'2

30 6

35 '6

40 '2

47 '3

59 '1

6 '1

89 3

102 0

119 3

mm. 635

590

526

480

412

359

327

300

263

(211)

195

150

130

107

Temperature, 100? o 0 707

5 2 651

103 601

16 9 543

24 2 485

28 '2 455

40 '3 (376)

54 '1 343

74 1 300

83 4 282

108S8 238

0 -00809

0 -0082

0 '0081 o 8

0 '0082 0 -0082

0

0 -0082 -C

0 '0081

0 -0079

0 -0078)

0-00499 :

0 '0049

o o0050o c3

0 -0049J I

min. nili .

0

6

15

21

30

38

50

62

74

87

104

116

123

142

187

C.

0 '00729 00

0 0067 0 I1

0 0066 |

0 -0064J

0 '00279 ? 0

0 0031 o

0 0029 1

oo c3 0 "0031J ,

0

1

2

4

7

13

20

27

33

43

54

Temperature, 175? C. rniln.

0 0

6 '2

14 '4

21 '3

30 -2

37 -5

49 9

62 1

76 4

88 *2

106 '5

118 '5

125 3

145 '0

188 '9

Temperature, 0'0o

1 '1

2 '0

3 '8

6 '4

12 3

19-7

26 '7

32 7

42 -8

53 7

724

683

632

592

545

508

452

403

352

315

265

230

212

168

100

250? C. 712

688

670

635

588

494

397

308

248

172

116 - -

min. 0

4

10

15

23

30

35

40

48

66

89

101

119

0

5

10

17

25

30

55

74

84

105

0 '00421

0 '0040

0 0041

0 0041 o0 o '0041

0 '0041 = o

0 '0042

0 '0041

o 0042

0 '0051 1

0-0051 J

0'0051J S

0'014 '

0 013 >

0 '012 0

0'012 R

0 012

0'013 j

0 -01579 ;

0 0157

0 '0157 0157

0 0157J J

I i

i




Series III.-Temperature, 140? C.

Ti

Observed.

ime. .... .- Pressure

Calculated observed. from mean values of K. I

Outside of Tube.

min. 0'0

5 6

14'1

29 9

48 '8

63 1

73 1

83 9

108 '2

129 -0

161 '9

mm.

735

721

700

663

621

591

571

(550)

523

501

468

0 -0014'

0 -0015 1

0'0015

0 0015 11

0 0015 1

0 0015 c1 o 0015)

0 0009. "

I o? 0 '0009 .?

0 0009J 11

min. 0

43

58

68

102

117

153

Inside of Tube.

min. 0 0

7 7

23 2

44'9

58'0

68 2

99'3

101 '8

118 '3

153 1

31

56

103

164

198

223

(293)

296

315

353

Time.

Observed.

155

Pressure observed. Calculated

from mean values of K.

K I log -i).

P:.- I?

K

(1log 76?-). \t 760 -p

min. 0

6

14

29

49

64

74

108

123

159

0 .00190)

0 00197 1 0 '00204 9

0 00196 i

0 00196 |

0-00196J

0 '001041 n.

O 000119 8

0 00112 J t



the diffusion of hydrogen through palladium

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